Cheapest snowy place to spend New Years on a holiday?
Lapland [the Lappi province of Finland]. The very first snowflakes fall to the ground in late August or early September over the higher peaks. The first ground-covering snow arrives in average in October or late September. Permanent snow cover comes between mid-October and end of November, significantly earlier than in southern Finland. The winter is long, approximately seven months. The snow cover is usually thickest in early April. Soon after that the snow cover starts to melt fast.
You need to do a search. Most of Europe is enjoying mild weather. UK None here forecasted.
They'll be popular and therefore won't be cheap. If you haven't booked by now you may as well forget it.