I love skating on my own, as much as I enjoy skating with the friends I have made over the last year. I find that sometimes, as someone else mentioned, I spend more time stood chatting than I do skating, but I also have some good friends that have helped me improve and encouraged me greatly. My forwards and backwards crossovers developed more through the help of friends than they did through lessons.
However, I also enjoy it when I manage to get to the rink for a lunchtime skate and there may only be a handful of us on the ice. I get on and do my own thing and enjoy the peace and quiet.
Having said that, I had the rink at Milton Keynes to myself for an hour last year. Just me, in my hockey gear (I was alone on the ice and so the manager allowed me to put on my full body armour), and I was so excited at having it all to myself I wasted the whole session tooling around and going as fast as I could, rather than focusing on things I should have.