FWIW, many report excellent results from grooving their R4's for use in snow, with pretty much zero drawback. I'd start there, since the grooving iron is less than a set of chains, and was reported to improve traction for most to the point that chains weren't even necessary... If that isn't enough, a set of chains for the front should take care of any remaining traction issues, and is, as you note WAY cheaper than chains for the back.
Tire grooving TBN Megathread
For the grooving tool, search "Ideal tire groover" on ebay. I think they're $80-100. I got two different blade widths for mine... One narrow, like 1/8" or slightly less, and one wider, perhaps almost 1/4". I have grooved almost every set of truck tires I've owned since I bought it. Helps me get another winter out of them after they're worn below 50%.