Mark,
I played at Prestwick in March (it was cold (2 C), it was snowing (just up the road there were drifts) and windy but magnificent) and we were not able to eat in the members Dining Room, despite being in jacket and tie. We did drink in the members bar afterwards. This isn't a complaint of any sort, by the way, we were treated extremely well by all, in particular by the lady behind the bar who served us plentiful Kummel and then brought out some cake she had baked. We were last to leave the bar, long after the last member but at no time did we feel anything but extremely welcome. Prestwick is one of my favourite golf clubs.