Well, we just moved the Tampa area, so winter isn't much of a concern for us
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I ended up taking her to a Specialized/Giant/Felt dealer and tried a bunch of bikes. Most of the 20s were just a tad too big, but the 16s seemed small, and I didn't want to spend full $ on a new bike that she'll outgrow in a few months if I didn't have to. Then I found a 2nd hand bike shop nearby, and they had a used Hotrocks 20 for sale for only $45. It was a single-speed 20", which looking at the Specialized website archive they only made in 2008. Surprisingly, with the seat lowered nearly all the way she fit on it real well, the old single speed frame must be slightly smaller than the current 20" Hotrocks. I did try Craig's List, but they were all either Walmart junk that I could buy new for the same price, or too far away to make it worth the drive.
I tried taking off the pedals again, and she was doing fine, but after about 30 min she was whining about how she wanted her pedals back. I put them back on, and she can ride it fairly well... until she gets scared. I'll hold on to her seat with my hand, so she can't feel my hand and tell when I let go. She rides perfectly without me holding for 2-3 houses, but as soon as she realizes that I'm not holding any more, she panics and puts her feet on the ground, which causes her to lose control and occasionally tip over. Oh well... every day she gets a little better. Hopefully if she stays motivated and gets over her irrational fear, she'll be riding well enough within a few days.
I really hope she does, because I just got the wife a bike as well, and if the daughter finally starts rolling then we can all start riding together. There's a real nice park only about a mile's ride away, with dirt and paved trails, playgrounds, and even a dirt BMX track. If she rides well enough that we can start increasing distance, and her single-speed bike becomes a limiting factor, I'll look at getting her something more elaborate.