a lot will depend on what and where your plowing snow
most 4x4 atv's will push decent amounts of snow on stock tires just fine, NO need for lockers or chains
if you get a lot of ice , all the more so if hilly, chains will be a big help, and or a dedicated set of tires that are studded!
to plow snow, I think you will be much better off with stock size tires 25-26's
27's and up will take a lot of the power away for the hard work of pushing snow
also, you do NOT want really aggressive tread tires for plowing snow, they will ONLY work in deep wet snow, in basic snow or in plow paths, they don't grip well, as they don't have much surface area on the ground, plus most are of very hard rubber and as such, don;'t work well in cold weather
a GOOD all terrain tire will work better, the key to working in snow and ice is LOTS of small edges grabbing and gripping for you!
look at any dedicated Snow tire, and you will find they are NOT big aggressive tread mud like tires, and there is a reason for this!
as for tire suggestions, , Big horns, bear claws and so on like treaded tires are liked by many!
work well all yr round, but AIN"T great mud tires!
there is NO one tire does it all great, have to compromise some times!
20+ yrs of plowing snow with atv's and many more yrs of just plowing snow
things to keep in mind, its better to plow a few times in a snow storm, than TRY and wait till it all stopped, DEEP snow, , all the more so can make the atv NOT able to push it, pending HOW deep[ and wet it is, NO matter the tires or chains
if snow gets very deep, or wet, many times you need to ADD weight to the ATV, to get it traction/down force!
remember ATV"S are designed to have a low ground pressure foot print by design, so when plowing, some added weight can be a BIG help, in deeper or heavier snow!
when lifting your plow with a winch, be EXTRA careful to NOT over IN on things, this is the #1 thing that causes winch like to break, be it SYN line,. or wire rope line!