Wow! Seems like there are probably more opinions on this than there are options! I have no experience but from everything I've seen, heard, or read the R1 Ags often will get caked with snow between the bars and turn into narrow donuts of slick compact snow. It's totally different with chains of course. Turfs have a wide footprint which gives a wide surface area for more friction and grip. And turfs are not like normal vehicle "all-season" tires. They usually resemble serious snow tires for a vehicle. Now LSW ("golf course") tires are pretty slick with very shallow lugs and would likely be horrible in snow. I would think that R4 industrial tires would do pretty well in snow. I would also think a lot would depend on whether you have 4WD or not, the weight of the machine, conditions of snow, whether the tires are loaded or not, and type of snow as well as the depth of snow. I guess that's why there's so many opinions of the subject.
Disclaimer: Note that all of this comes from what I've heard and from educated reasoning; I have no personal experience.