Visiting the Lake District in winter is an amazing experience for anyone who loves walking and enjoys the magnificent scenery that the Lakes have to offer. The weather in that area of the UK is usually going to be cooler the further north you travel but as long as you pack the right clothing this should not be an issue, remember there is no such thing as bad weather only inappropriate clothing.
The key to keeping warm in the great outdoors is layers and plenty of them. Thermal underlayers are a good idea both for the upper and lower body and remember that lots of thin layers are better than a couple of thick ones as body heat is trapped between the layers keeping you warmer.
A waterproof and windproof coat as a final layer is necessary as the weather can change quickly and you will be more comfortable if you are warm and dry.
Having the correct footwear is vital to the comfort of your experience. Walking boots or shoes should be worn in if possible before any long-distance walking is undertaken and should fit well to avoid rubbing. Socks should ideally be made from a natural fibre such as cotton or bamboo to prevent your feet becoming too hot and sweating.