I was on Tenerife the last week of December and first week of January two years ago - no snow at all.
I was on La Gomera in the same time frame last year - a little on Teide, though it seemed to be very little.
I was on La Palma in February 2004 - big snow and ice - I think the picture above is taken from that year. Actually I think you might have required crampons and ice axe in that year.
Bottom line - you can never be sure but in General Tenerife is pretty weather proof during the holiday season. You might find rime on the roads to the Canadas and this might already turn you back because the rental cars you get on the island never have winter tires. You'll most likely won't need any winter equipment except for warm windproof garments. Even when it is 25°C at the coast you'll have freezing temperatures up there and almost always fierce winds.
What you need, however is a permit. Oherwise the rangers won't let you climb the remaining 150 m from the Rambleta, where the cable-car ends. You also will have to try to acclimatize. Living at sea level, driving up to 2100m and then climbing to 3700m all in the course of 3 - 4h will take its toll. My body always revolts by producing incredible headaches so you might want to bring a pack of aspirin and lots of water to drink. Water is rare in the Canadas - the whole crater is a desert. Don't expect to be able to buy anything at the cable-car or anywhere in the Canadas, the nearest bar / restaurant is at El Portillo in the nort of the crater.
Accommodation: There is only the Refugio Altavista and there is no service there, at least in winter. So bring your sleeping back, climb to the refugio at night, stay there for the night and climb Teide in the early hours of the morning. That way you might be able to bypass the permit problem - plus yoou''ll have the most beautiful sunrise of the Canarias.
Other mountains in the Canadas could serve as substitutes if Teide should be covered in ice. Just go to the
Tenerife page and click the mountains in the left sidebar down to Roques del Cedro.
For an impression of what the weather was like two years ago see the following Trip Reports:
Dancing on Lava
Crossing the Desert