To mow or not to mow?

Hi all, just after some turfing advice. We had turf laid in the last couple of weeks of September (garden was originally all gravel from previous owner) and I thought it would be fine to leave it for winter and not touch it to bed in properly.

However it has since gone bananas and has grown several inches since being laid which I’m guessing is a good result (despite the local cats now using it as a toilet!).

Question is should I mow it now with winter coming or just let it grow away until next spring?