Ski poles with a good grip system will save you a ton of money, be very lightweight, durable, and can take the abuse of winter slush and mush. A big advantage is that they will go into the surface with a good bite, not just on top of the surface.

If you want to try them, visit a used sporting goods store or ask around, I'd bet one of my ears that someone you know has a pair collecting dust. Check the strap, you want a solidly attached, preferably adjustable nylon web, and hand grips in good, solid condition. They're not pretty but highly functional.

Trekking poles are another trendy, pricey option, but for the level of use in your case, ski poles are ideal.