but a true CX bike doesn't have mudguard eyelets, so a bit pants for winter, albeit you can fit clip / strap on ones.
back to the OP
Yes it makes perfect sense. You already have a summer road bike so why not get something slightly different, with two sets of tyres (and possibly 2 sets of wheels (but you may be able to swap your other road bikes wheels in and out depending on QR vs TA disc vs rim 11 spd etc etc), a "call it whatever term you like" bike that has mudguard mounts, wider tyre clearance and slightly relaxed geometry is the most versatile thing you can buy.
Even if you don't do much of it, the joys of the occasional traffic free ex railway line / decent surfaced bridleway makes a refreshing change