i dont think i have started to get fat arms - or, if i am, it just sorta blends with the rest of me. But, i think water aerobics have helped abit thou.
I would do arm exercises to firm up. If you dont have weights, perhaps try using tins of food for weights, or putting sand or water into bottles. Then do a few different sets of repetitions a day.
Or, just hang out till winter, and cover them up