There is probably a 95% chance you will be fine with just turf tires. I have used all 3 types on various tractors and this is my overall conclusion. Turfs- best of the 3 on hard packed snow. R1 ags work great on deep snow or breaking new paths but tend to slide easily on hard pack. R4 industrial- I liked these the least. Not enough traction in deep snow and still slide on hard pack. R4 was the only tire that I needed the assistance of having chains.
Unless you are working on very steep slope you should be ok without chains as long as you have 4wd. Plow trucks rarely if ever have chains.