I don't think it is good idea to keep basement window open in winter. If you do so, your water pipes will be frozen and cost more to repair. Install a radon fan is a better choice. It is not so difficult, it would cost less DIY - around $600 - $700 (fan, pipe and install kits + tool rental) depend on your basement. If your basement has rough-in (most new houses have), it will be much cheaper.