Like the OP, I started out in FL, so I can relate to the cold water adjustment - first doing a semester in South Australia and then relocating to Southern California (after that I put in time in Puget Sound, which was enough to convince me I belonged in the tropics). Beach entries and exits were also a new wrinkle.
In Southern California I wore a 7-mm suit with a built-in 5-mm vest and hood. With an AL80 I used 16 lbs on the belt plus my 6-lb steel backplate; when using an HP100 I cut that to 8 lbs on the belt. Then again, I'm one of those people who can't do a dead man's float - everything south of the ribcage sinks. In FL with a 4:3 suit I typically don't even bother with a weight belt (still have the backplate; if I'm diving with my old LP120 water heaters I upgrade to a 40-lb wing to give myself some reserve buoyancy).
I don't recall having many issues on my beach dives in SA, but my first one in CA - Shaw's Cove - ended amusingly. I was wading out of the surf with my fins in hand and unfortunately, my reg was not in my mouth. The pull on my legs was my first hint that things were going to go sour and then I got knocked to my hands and knees and forced under. Stayed calm, held my breath, and then once the water receded I made sure to pop my reg back in while I trudged up and down the surf zone looking for my fins. Probably had a few other times where I got knocked arse-over-teakettle in the surf, but at least then I remembered to keep my reg in.
Probably the biggest issue I ever had with cold-water diving was having a mask flood. The first time I really had my mask severely flood with 58 F water, I tried to breathe normally and couldn't - at the time I thought my regulator had crapped out. Turns out getting cold water on my face was enough to make my breathing reflex shut down; I had to consciously command myself to take a breath. When I did skills checks in Puget Sound, mask-clearing was challenging for that reason.