Is starting an extension in February a terrible idea?

[Endlesslllove]

We've been planning an extension for ages, looking at starting the work in March. the builder we were going to use has had a delay so can't start till June now. Other builder says he could start in two weeks! I wonder if the reason he's free in February is because no one else wants work done in such a cold month! (He's highly recommended otherwise). I'm worried partly about the house becoming freezing once they knock through, and also if it rains it won't dry out much if temperature is around zero.
The extension will be a first floor one, building above our kitchen to make bigger bedroom & bathroom. I'm keen to have it done asap (have 2dc and running out of space), but then again we've waited ages already so could wait until spring if that's better.
Is there any reason why building in v cold weather is a bad idea?

We started our extension in January. The builders were working in the snow at some points. It was ok for us as they didn't knock through for quite a long time. Most of the extension building was completed before they started making holes in the walls to connect it all.
If your builders can work like that you should be fine.

Thanks Lindy that's encouraging