We secured a volunteer position at a Florida State Park between Gainsville and Jacksonville on our first try. We didn't even try at the southern parks. I did maintenance 20 hrs a week, did general carpentry, power washing, painting, tree trimming, invasive plant removal, sign replacement and more. We stayed 5 months.
Try the northern parks, write or call the parks direct and ask to speak to the VC everyone wants the south, not so many the north but it's still better than snow country. If I recall our lowest daytime temp was 48 and about 10 nights that got below freezing.