In reply to RatKing:
All you can do is go where the weather looks best. The best bet for winter conditions is always going to be Scotland, although even there you'll be lucky to get much before December. But, you can sometimes get full-on winter conditions in November.
Scotland can be really windy in the winter. It pays to plan your day around wind speed and direction.
If you don't already know the MWIS website provides (a generally pessimistic) mountain weather forecast for the UK, including links to avalanche forecasts.
Any of the Munro outings in Scotland are transformed in winter to something significantly more serious. That said, especially in the Cairngorms, I'm not sure 10km will get you very far. That would be the Linn of Dee to the Derry Lodge and back. You can always take a bike if you have one.
As others have suggested, if it does snow early this year, you are more likely to be ploughing through soft, fresh stuff than striding along in crampons. It'll work wonders for your fitness though! Assuming you don't give up and turn round.
Realistically, get to Scotland if you can and don't worry if there is no snow, but if it's too wild (i.e. wet and windy) there head to the Lakes or Wales. The Peak is a last resort.
Post edited at 20:42