Our club do weapon work about once/week and it is all outside. We're quite lucky 'cos we can do it on University grounds. We've also done it on the local beach (and many people practise ukemi on the beach) but there is a possibility of being arrested for carrying an offensive weapon if you're not careful (so we tend to hide away somewhere).
Great thing about weapon work outside is it is less dangerous 'cos you have more space and you can do massive long Kumitachi without fear of running off the end of the mat or hitting someone. Also there are interesting variables like direction of the sun and uneveness of the ground to think of. (and you also get a nice tan).
I've yet to try some bokken work in a forest, but I think that may be a fun experience!