Reading some of the comments on this answer:

....they're seen in the UK as winter birds.Not, I think, that they're not around in the summer; more that other birds aren't around in the winter but robins are. Robins are often found on Christmas cards in the UK. (Christmas being in the winter in the UK.)

Robins are around all year in the summer, spring, etc. and have a red breast, etc (except juveniles) all yea, RSBP web site confirms this:

The UK's favourite bird - with its bright red breast it is familar throughout the year and especially at Christmas! Males and females look identical, and young birds have no red breast and are spotted with golden brown. Robins sing nearly all year round and despite their cute appearance, they are aggressively territorial and are quick to drive away intruders. They will sing at night next to street lights.

So why are robins so associated with Christmas and winter? Where does this come from?

Reading some of the comments on this answer:

....they're seen in the UK as winter birds. Not, I think, that they're not around in the summer; more that other birds aren't around in the winter but robins are. Robins are often found on Christmas cards in the UK. (Christmas being in the winter in the UK.)

Robins are around all year in the summer, spring, etc. and have a red breast, etc (except juveniles) all year. RSBP web site confirms this:

The UK's favourite bird - with its bright red breast it is familiar throughout the year and especially at Christmas! Males and females look identical, and young birds have no red breast and are spotted with golden brown. Robins sing nearly all year round and despite their cute appearance, they are aggressively territorial and are quick to drive away intruders. They will sing at night next to street lights.

So why are robins so associated with Christmas and winter? Where does this come from?