A 2k budget probably won't get you a very decent machine, at least here in Idaho it won't...you may find a 30 year old machine that has been rolled a dozen times, missing most of the parts to make it move, blown engine, etc. LOL.
I've had 2 Yamaha products, they were fine but their customer service and finance company put a stop to me ever dealing with them again. Polaris is big around here because of parts availability and aftermarket accessories, something that Yamaha seemed to be lacking at least for my Yamaha Rhino side by side.
One thing with the Yamaha's I had I didn't need 4WD very often just due to having a locked rear differential. Polaris has a bit of an edge as some of their machines have what they call turf mode which gives you a selectable open or locked rear differential plus 4WD...which really is misleading, the machine is only in 2WD when 4WD is engaged until the rear wheels slip a certain amount then the front axle is engaged, then it goes back to 2WD again.
Honda has been making ATV's for what seems like forever, possibly the first manufacturer to make them? Anyhow, they're pretty good underpowered a bit but at the same time less power usually means you aren't going to break anything, where Polaris for example has 1000cc engines and things tend to break easier and more frequently due to the added stress from the extra power of the larger engines. My Yamaha Rhino was a 700cc it had plenty of power but I would say it was adequate for the intention of the machine being a sport/utility machine.
Polaris has issues with their CVT's (continuously variable transmission) eating belts in some cases due to riders using the wrong transmission range and causing belt slippage which results in burned up drive belts. Their CVT's do not have a one way clutch so the belt slips continuously until enough power is applied to engage and its usually a very sudden jerky engagement from what I remember. You are also limited to low range for a lot of usage of those machines as a result of the transmission setup.
Yamaha's CVT's have a one way clutch allowing the belt to stay engaged all the time regardless of speed, this allows you to use either high or low range for any application regardless of speed or load. Also gives you far superior engine braking enough engine braking that you can lock up all 4 wheels in 4WD going down hill in low range.
I cannot speak about Honda's drive systems as I have never been around any. I know earlier automatics were really terrible and were never in the right gear and would seem to get stuck in too high of a gear causing you to lug the engine and eventually stall it. I'd stick with the manual tranny in the Hondas.
I'm not sure if its offered in Yamaha products anymore but they used to have a semi-auto transmission which was nice as it gave you gears but with an automatic clutch, pretty reliable system.
Yamaha has a 2WD/4WD limited slip/4WD Locked differential mode in several of their ATV line. Older models had 2WD/4WD limited slip. I found that 4WD limited slip took me into places just fine never felt the need to use the 4WD locked differential mode, I did play with it a bit but steering is horrible in locked 4WD. The Polaris system is simple you could leave it engaged in 4WD mode all the time and let the system figure out when you need the extra traction, or you can chose 2WD or turf mode. The turf mode would be one reason I'd chose Polaris because it is great for utility work and won't tear up your yard. I know a few of the Polaris Sportsman's had the Turf Mode option, not all of them did though so you would have to look at them to see for sure...it'll have a switch on the handlebar that has turf mode, 2WD, 4WD settings.
I really don't think you could go too wrong with any brand machine especially in your price range because for what you want to do they'll all do it, hell even a 2WD model will go places you'd be surprised at. 4WD just gives you a bit more assurance and in some cases stability having all 4 wheels receiving power to help pull you through where a rear wheel spin could get you sideways on a trail very easily.
I used my Yamaha Grizzly 450 4x4 ATV for plowing snow occasionally and it had plenty of power to do so. You don't need a huge machine for plowing snow, and in many cases a smaller machine is faster as its easier to maneuver a smaller machine in cramped quarters. For plowing though a fully automatic transmission or CVT is the way to go...trail use a manual or semi-automatic would be the way to go...however those CVT's are pretty dang reliable if you use them properly.
Welcome Visitor! Please take a few seconds and 
