Snow is a tricky subject, even here in Michigan. I have little interest in getting into the snow side of this business, so I just sub all that work out to a few friends who plow. However, I only work in the landscape industry part-time, I have a couple other things I do that keep me busy (college classes and part-time work as a firefighter/paramedic).
There are plenty of opportunities out there that you can add to your business to make your "off season" a little more productive and profitable. Christmas decorating is becoming a very big thing for some companies and if you have the skill and the desire, that can be a very lucrative business. You can also look into landscape lighting services. If you don't get much snow, this would be a good time to do things like the landscape lighting, when you aren't so busy with mowing or doing spring/fall cleanups.
The winter also offers you a good opportunity to start some advertising for the next season. Get ideas for door hangers, flyers, websites, networking, etc.
Budgeting is going to be an important part since you are in a seasonal business. You NEED to plan on making enough money during the normal mowing season to get you through the winter. Think of any work you pick up during the winter as "bonus" money, put that in the bank, reinvest in your company, etc.
'07 Chevy 2500HD
2010 John Deere Z925A 54" MOD
2011 John Deere Quik Trak 647A
John Deere walkbehind