Wouldn't הסוס שלנו or just הסוס be a bit more colloquial?
Absolutely, but it's under Possessives 2, the entire unit discusses such constructs.
What's the difference between 'סוסנו' and 'הסוס שלנו'?
Accordingly to Tips and Notes, it's the same.
The purpose isn't to teach a new kind of possessive, just a new way to construct a possessive :)
Which way of constructing a possessive is more commonly used in Israel? (For all situations, not just carrot-eating horses :-) )
According to tips and notes the genitive case construction is formal, and the other is more used for every day's language
For כי can "for" be an acceptable word?
It would be understandable but archaic English
As good a reason as any