Oiling won't help. I've had this problem the past few years on my car. The best bet is bring something along to tie unused doors shut. Seems the latches on these cars were horribly designed.
Most likely, the latch isn't frozen but gummed up from previous lubrication. What I have had okay success doing is putting a heat lamp on the latch (making sure to not burn the paint / melt anything) and let it sit until everything gets nice and toasty.
Then take the heatlamp off and spray carb cleaner or brake cleaner avoid breathing on the latch.
This usually gets me a week or so of functioning door then it stops working again.
I'd rather have a rustbucket than a rice rocket!