We went in late autumn, so never tried the pool. You'd be better off getting a definite answer from the manager. I'm afraid my experience of the hotel facilities was not a good one - on a two night dancing break the dance-floor turned out to be only available for one night. Never did get any kind of apology.
Yes, it wasn't it use when we visited but we were told it was heated.
Get an answer from Livermead House Hotel staff and past guests.