Tenerife is very busy during the winter months with all the 'snowbirds' - retired people who stay there for 3 or 4 months to escape the weather in the UK, Germany, Holland, Belgium and of course Spaniards like to holiday there as the weather is so much better than mainland Spain.
Everything is open, all the buses and trains are running.
All the British bars will be open serving Christmas dinner, full English breakfasts and fish and chips.
Saga have hotels in Tenerife and walking holidays in Lanzarote.
http://travel.saga.co.uk/holidays/special-interest/walking/walking-in-lanzarote.aspx?bb=AI&duration=7