I have solar panels in the central New York state area - we get an average of around 120 inches of snow per year for reference. Production is lower in the winter but the snow usually melts off the panels within a couple days after each snow storm - even less if you broom the heavy snow off.
The first step is to see where you can cut your energy usage. Many contractors near you should provide you with a free home energy audit - this usually involves a blower door test and use of a thermal imaging camera. It can highlight air leaks from your home where you may need to add insulation. A well-insulated home costs less to heat and cool and insulation has a faster pay back than solar panels.
For solar, you need to check the specific incentives for your state and how the excess power is billed. In New York state, for example, there was the 30% federal tax credit plus an additional 25% state level tax credit (up to a max of $5,000) - so depending on the size of your solar panel installation and your tax situation, this could be ~55% off the top line price in NY. Also, New York requires utilities to offer net metering, so any excess power generated during a particular month (such as the summer) rolls forward to future months with a once per year reset date. This means you can generate the power you need for the winter over the summer. In addition to state incentives, there are also sometimes more local incentives or programs. Our county had special group buying discounts periodically that gave extra rebates if you bought your panels at the same time as others in the county.
Once you know what state incentives there are, you should get estimates from many different installers - they should be able to provide estimates about how much power different panel set-ups would generate. Depending on space, you may be able to offset your entire annual electric usage.