So we are building our garage into a living space. It will have a kitchen and bathroom. I would like to just keep it one big open room and do a mini-split but since I'm "rooming off" a few areas I guess I'll need to run ducting into the main areas with smaller ducts going into the rooms to get the air/heat around.
Why? As long as you have windows with vents, you should be fine. Cut your doors so there's a little bit of a gap between them and the floor. Put a mini-split in the living area, a heat-light combo in the bath, and nothing in the kitchen - the appliances and heat from the other room should be sufficient.
It is on a slab. We are in TN so it doesn't get incredibly cold but I feel like the slab temperature will be an issue in Winter (cold to feet). I thought about trying to tie some kind of radiant heating (water based tied into the hot water heater) into the floor but guess I'll need to either cut channels into the concrete (sounds like a lot of work) or raise the floor somehow?
I'd do electric floor heat if you don't have a boiler already setup and you aren't going to need it much. Carpets or wearing shoes indoors are also an option. Raising the floor isn't an issue - build your radiant system (usually 1/2-1"), put a floor topping of your choice on top. As long as your ceilings are at least 8'-0" already you won't notice. Be aware that concrete/tile work best with radiant floors, then wood, not carpet.
Or is there a way to "insulate" the floor somehow so that it doesn't get so cold? Just looking for some ideas to do this economically.
Short of tearing it out and redoing it, carpet (or rugs - I prefer those as you can replace them easily if they get old, and take them outside and beat them senseless if they get dirty). You might be able to put other insulation above the slab, but that isn't standard practice. If it's really a slab and not a footing under the wall with slab floor, insulation around the edges of the foundation should help - most heat loss in slabs is at the edge, not the middle.
I guess electric floor radiant heating would be thinner and easier to cover but I've heard the bills are high with that. Anyone encountered a similar challenge with their project? Thanks!
Yes, but you should only need to run it briefly if you've also got the mini-split and you're living in a small garage. Turn it on just enough to heat up the slab and keep it from being cold, and usually only when you're in bare feet - say, in a bathroom in the morning.