Overall, I am in some ways sympathetic to the project Michael Horton is attempting in Introducing Covenant Theology. I would say I like the idea of it all, but he leaves many questions unanswered. I would consider myself Reformed in my theological leanings, or you could use the word Calvinist(ic) if you wanted to. However, I am not entirely convinced the case Horton makes here holds exegetical water. The book does follow a fairly logical flow, but that might not be enough in the end to overcome the exegetical errors.
Horton starts with the big idea of covenant theology, then in the next chapter moves to the ancient Near East background of the concept of covenant. In chapter 3 he starts dealing with the biblical data on the matter using the lens of Paul's allegory in Galatians 4 of the two mothers. His conclusion is that there are essentially two types of covenants, unconditional and conditional, which roughly correspond to promise and law respectively. In chapter 4, Horton elaborates on the new covenant and explains where there is continuity and discontinuity between it and the old covenants in the Hebrew Scriptures.
At that point, the discussion in the book then shifts to unpacking the basics of covenant theology as a system of interpretation in chapter 5. It is here that Horton addresses the traditional Reformed covenants of redemption (intra-Trinitarian), works (between God and humanity), and grace (between God and the elect). Chapters 6-9 then unpack the implications of this understanding starting with how to live the world in light of common grace (chapter 6); how the covenant people are constituted (chapter 7); the signs and seals of this covenant of grace (chapter 8); and how we are to live in light of it all (chapter 9).
I like many of the things that Horton says throughout the book, and like I said, I am generally on board with covenant theology, or at least would not consider myself dispensational. Horton does not do the best job in the book interacting with dispensationalism and at times makes sweeping statements about the view for which he offers no support (pg 129 for instance). This is perhaps ironic, for Horton had earlier opined that O. Palmer Robertson said something without a supporting footnote for which "it would be very difficult to find a credible Reformed theologian, past or present, who holds this view" (pg. 102-103). Overall though, his rhetoric is not out of line, he just does not really interact with opposing view very much.
There are however some deeper problems. Most notably is his treatment of covenant in general and Genesis 15 in particular. To start with the particular, it would be a little too nit-picky to hold Horton to the standard of being on the forefront of biblical studies and scholarship since that is not his field. That being said, there are a couple of glaring errors in his treatment of Genesis 15. He sees this narrative as the most important example of the nature of the Abrahamic covenant (pg. 40). He quotes Delbert Hillers at length (whose book was written in 1969) concerning how it was customary in the ancient Near East to walk through the severed pieces of animals to ratify a covenant (pg. 40). He had previously noted in regard to suzerain-vassal treaties that they were ratified in the same fashion (pg. 28). While the oath and slaughter of animals is present in many ancient Near East treaties and covenants, the walking between the animal parts is not. After reviewing all the extant covenant making texts from the ancient Near East, Ake Viberg makes the observation that "None of them presents either a divided animal or someone partaking in the covenant by walking through the parts." Or in other words, a more careful recent study has shown fault with earlier assumptions (and they were only assumptions for the most part).
This may be a minor quibble, but considering how often Horton references Genesis 15, it is at least significant that it is not a typical demonstration of an unconditional covenant, and the ritual may be more at home in other ceremonies. More importantly, as Gordon Johnston noted in paper presented at ETS a few years back, there are syntactically different ways of referring to a covenant depending on whether it is primarily conditional or unconditional. Careful exegesis would bear out that the unconditional formula is used in reference to the Davidic and New covenants. The conditional formula is used in reference to the Mosaic covenant and in reference to the Abrahamic covenant only once...in Genesis 15. A bit of an oversight it seems on Horton's part.
Shifting from the particular to the general, there are two projects Horton needs to address to make his case stand: (1) outlining a valid definition of the Scriptural term(s); and (2) a principle for the acceptable use of the concept of covenant. Horton is right to point out that one can speak of covenants even in absence of the word (e.g. "berit" is not used in 2 Samuel 7 or 1 Chronicles 17). However this still leaves open the issue of when it is appropriate to use the concept "covenant" to describe what is going on in a particular passage. In the example just mentioned, while the actual passages do not use the word, other passages do in connection with them. It may then be better to say that one shouldn't press hard for describing a reality as covenantal when Scripture never does. It may be helpful to do so in order to unpack the meaning, but that is a bit different than insisting that covenant is the underlying reality of a given passage.
Case in point, the two controversial examples from covenant theology are whether or not it is appropriate to speak of a covenant among the persons of the Trinity concerning the redemption of man, and whether or not it is appropriate to speak of Adam's relationship to God in the garden as covenantal. Neither incident is spoken of in Scripture using covenant terminology, nor does it seem any specific writer of Scripture conceives of those two realities covenantally. In the case of the Trinity, Horton oversteps the exegetical data in arguing that the covenant of redemption is a revealed teaching of Scripture (pg. 80) and is as clearly revealed in Scripture as the Trinity (! pg. 82). He does admit that Scripture "knows of no suzerain-vassal type of treaty between the persons of the Trinity," so then argues that we cannot have to restrictive of a definition of "covenant." This though seems to go against his modus operandi of using exegetical data to support systematic conclusions (pg. 12-13, 23, 77). If we are going to go with how Scripture defines covenant, then it is inappropriate to call the plan of the Triune God to save his people a covenant among the members, since Scripture never conceives of it that way, and the usage of "berit" does not fit a relationship among divine persons. If we are going to loosely define covenant in a way that allows us to cover everything that fits our system, then that is a different story altogether. While Horton had stressed the importance of not using systematic theology to impose a system on Scripture but to draw out the main teaching of Scripture from Scripture itself, it does not seem his own work here accomplishes that task.