Another vote for a cheap winter beater. I suspect you'll end up spending more working out alternative solutions, or worse, risking your life to save a few dollars.
I also live on a rural blacktop, approximately 20km from town and in an area where winter can last 6 months. During peak winter, days are short so it's dark in the morning, and dark in the evening. Visibility is limited and motorists are half asleep on their commute in, and their minds are 'at home' on the drive back. Or worse, they have the sun directly in their eyes both ways. Not a good combo.
With icy roads, they can't stop anyway. And most are in SUVs and large trucks doing 60MPH with half-clear windshields and not expecting a cyclist. Even if you can find purchase with studded bike tires, you've got salt spray and slush from vehicles. Frozen ruts if you have any sun during the day.
And then weather to deal with. Here in the US midwest, there are days where frost bite will set in within 15 minutes exposure, slightly longer if you have the best winter gear. One tumble or accident and you literally risk your life due to exposure. And I don't know about plow schedules, but winging and shoulder clearing usually happens much later than primary pavement clearing. Not great for cycling, especially when snowing over black ice.
Unfortunately, I suspect your costs are higher than here. I can find a good winter car for $1k, with $100/yr insurance, and let a couple credit card bonuses cover all the gas and maintenance for the year.
