Depends on who's playing who, and what the status of the table is at the time. Man U vs Villa could be possible. Arsenal vs Spurs would be a lot more difficult because that's a local derby and they're fierce competitors. Tickets are definitely not cheap, especially if it's a clash between teams that are riding high in the table.
Snow is hard to predict for the UK, but somewhere around mid Jan through to mid Feb would likely be the most statistically likely tmie. However, it also depends where you are in the UK. London doesn't get that much snow, and indeed England as a whole can sometimes go entire years with no snow at all.
If you wanted to have more chance of snow, either hit the highlands in Scotland, Snowdonia national park in Wales or get guaranteed snow in the Alps, Pyrenees or Scandinavia. Budget airlines are very common in Europe; major players include Ryanair, Easyjet and (increasingly) Norwegian. Refer to http://www.skyscanner.net for information, but read the small print carefully, the rules are applied extremely strictly.