Originally Posted by kay

If they are sweet peas (ie scented), they won't over-winter. So pull them out (they come out easily) for tidiness, which is quicker than cutting.

There is a slight chance that they are perennial peas, which are not scented, and tend to be uniformly either light or dark pink, and tend to be a larger plant. If this is the case, then cut them, and they'll grow up again next year.

In both cases you are just doing it for tidiness - the plant won't mind if you don't bother.