The best lawn and garden tractor I have every used for snow was my dad's Gravely 8173 (which he still has). These machines are bulletproof and have rear engines for superior traction. They are getting a bit long in the tooth and hard to find, but Mark Shubert at Shubert Gravely in Newton, NC has a couple in stock that he took on trade. They might just fit the bill with either a blower or plow (you might be on your own with the blower). That machine would cost much less than your price range and would give you years of good service. Another alternative is to go with a previous generation 300 series JD (such as a 325 or 335). Air cooled mid hours versions of these would likely not be much over $4K in price and will run 1500 hours without much trouble in most cases. They would power a blower well. As for new tractors, I have had and operated a little X 360 JD and that is one nice little machine. It does not have diff lock, but it has plenty of engine power, power steering, and a hydro lift. It would easily power a SB and with chains and a weight box in back would do just fine. It has the heavier hydro tranny and is a really nice tractor. With the attachments you want, it would be a bit over your price range, but probably not by enough that you should not look at it as a potential machine.
John M