It is very possible to fatbike year round. It really depends on the terrain. If you ride rocky technical trails perhaps a dual suspension fat bike like a salsa bucksaw or a trek farley ex.
You may want to consider spending a little less than you would for all year bike. In the snow you don’t need a bluto or 1×11 transmission but something that you can pedal in the snow. Motobecane and Framed make good bikes for about $1000
Tire size, for snow I use 5″ for snow and 4″ for the dry.