Have a look at Cumbrian Cottages. They have a big choice. We stay at a lovely one in Ullsdale, which is a hamlet with the most fantastic pub! It is tiny and very out of the way, but the cottage is lovely. It is about 10 miles north of Keswick and a few miles from the A66, which is the main road. There are some nice roads to walk along there. It is quite high up and phone coverage is spotty at best, but its lovely. We love the Lake District.
Hawkshead. Lovely pubs, easy access to Coniston etc and Latterbarrow to walk up to - some steepish bits but very doable. Fantastic view of Windermere from the top. There's Tarn Hows over the other side which is picturesque and a dead easy short amble. For a longer walk you can park at the top of Coniston Water and approach it from Monk Coniston. Elterwater in easy driving distance. Park at the National Trust car park and either go left along the river or there's a walk out of the village past the old mines towards Little Langdale.
In the Grasmere area, a lovely walk from Rydal to Grasmere which is not at all hilly. From Grasmere you can walk up to Easedale Tarn which is a very beautiful walk but has a very good path. You can walk from Rydal to Loughrigg Fell - not too demanding.
Grasmere is close to Ambleside, at the head of Windermere, and Coniston/ Hawkshead/ Little Langdale are easy drives away.
The area around Keswick is great - not so busy as Ambleside, and better choice of hills. Catbells is a great little climb with fantastic views. Look at the village of Threlkeld for places with pubs to walk to. Very convenient and has the best cafe in the village hall. And you may well get snow, which is a massive bonus. Nowhere better than the Lakes in Winter!
I would say the chances of snow are very high, having spent a good time in the Lakes. There will likely be snow on the mountain tops and I'd be very careful of walking high if you're inexperienced. You need the correct gear and be aware that the weather can change very quickly. I've mountain walked alot in NE Lakes and sometimes in February. There's some fab routes but do make sure you can use a compass and map or stick to lower levels. Even something like Cat Bells (a popular, relatively easy ascent in summer can become very icy and slippy in winter). The Lakes is fabulously scenic, especially in the winter. Take care and you'll have a great time.
We have found the Grasmere area a great place for a base. Lots of great walks start nearby. If there's a lot of snow, there are some good low level walks eg around Grasmere lake, plus it's near-ish the park at Brockhole with its ropes course which our kids always enjoy. When the weather's really bad, there are shops/tearooms in Grasmere to while away the hours. However, I think it's hard to go wrong in general regarding location in the Lake District - so many beautiful areas.
Is it just adults or DC as well. Keswick area has something for everyone. If you prefer quieter maybe look at Hawks-head, Nether Wasdale, Eden Valley. Please don’t climb too high or if conditions are bad as mountain rescue all volunteers have to come out and try and save you.