one thing that I hated about my older steel CX bike, is that it couldn't run the fat tires without removing the fenders. With the fenders, the snow just clogged up on the canti brakes and fenders, causing extreme drag.

Since last year, I'm using new aluminum MTB with drops and it allows 26x2.1" tires, with fenders and plenty of room left over to keep the snow from building up.

MTBs have more tire selections and the frames and parts are cheaper.
If you don't mind having only SS, then it is entirely possible to make a cheap dropbar MTB that is much more worthwhile than trying to make a SS CX.