I think saddlebag+PunksTank+SEAmom pretty much covered it.
However, I wanted to add my own opinion because...I have one.
1) I think it's important for all young horses to be familiar with blanketing so kudos for getting your girl used to it.
Personally I'm not a huge fan of blanketing young horses due to the reasons Saddlebag explained. However there are a myriad of reasons why a horse might need to suddenly+unexpectedly be blanketed - illness, etc, and I wouldn't want to have to go through blanket training right then, in the heat of the moment!
2) I think it bears pointing out that while many horses are equipped to deal with the cold, some horses just cannot handle it.
My 27 year old girl, though she grows a winter coat envied by wolves/woolly mammoths, just cannot deal with any sort of chill. In her case, getting a chill can cause anything from weight loss - even with plenty of hay, to an ERU episode and costing her more of her already waning vision.
Physically she appears to be able to handle the cold - based on her coat, but in real life, being cold can have catastrophic results for her.
I certainly would not blanket a horse that could handle it but it's unreasonable to paint every horse owner who blankets with the same "that's bad for the horse" brush.
Anyway, I know, OP, that that does not particularly bear on your circumstance but it bears on the topic, I suppose.
Another idea for desensitizing your girl, OP, is to start with a fly sheet. Since it's still warm out, she might have a better reaction to something that doesn't add heat.... :)