If you have a Hybrid, you can mount "Fatter" tires. Probably. Perhaps 40mm tires + STUDS.
A 26" or 29er MTB might be able to take slightly wider tires. 60mm?
If you really want a FAT bike, then you'll have to get a specific style of bike. Walmart may have some cheap FAT bikes. Maybe not for heavy trail use, but it might be good enough to get a taste for the concept.