I had turfs on both my 16 and 33 hp tractors for 30+ years. Turfs give a nicer ride in the summer because they are soft, low pressure tires - and turfs have noticibly more sidehill stability. Turf tires do take a special wide rim to mount them on and those rims are costly as are the turf tires themselves.....but I think they are worth the money for the stability if nothing else. Our soil here is sand and rocks, so in the summertime the turfs can give traction as good or better than other tires. On rocks, the summertime trick for traction is friction rather than cleats.
Have you thought about flats? Most tractor tires are tubeless, but R4 and Ags can be hard to repair at home if they get a nail. Fixing those heavier tires often requires dismounting them from the rim. Turf tires are so soft you can repair them yourself right on the tractor with a tubeless gummy strip kit from the local auto store. Takes maybe five minutes and you're done.
My experience is that turfs certainly don't do as well as R4s or Ag tires in the snow. R4s and a heavy machine are best for snow, and everything works poorly on ice. But on a lightweight tractor you are going to be running chains in the winter anyway so the traction of the bare tire doesn't matter much. Chains do better on turfs than on bar tires because there's no space for the chain to fall between the bars.
Ags and R4s will tear up a lawn much faster than turfs, but some turfs are nearly as bad. THat's because it's the edge of the front tires that tear up grass and sod when turning. So the trick with turfs and smooth lawns is to make sure that your front turf tires are the kind with a rounded profile. Take a look at some in photos. The profile of front turf tires is very different among different makes. The ones you want have a very rounded edge; in fact they might not even have a discernable edge at all. Sort of balloon fronts. If they aren't that kind, try them on your lawn. If they work, good. If not, you already have the rims and it's not too badly expensive to buy nice round profile front turf tires. It's not like buying rear turf tires - that can be shockingly expensive.
enjoy!
rScotty