Make a "cooling coat" for my doggie? (doggie pictures included)

⭐️MerFerret⭐️ • Beagle mama • Lupus & Fibro • 🏳️‍🌈 bi
I was thinking of making a cooling coat for my doggie because she seems to get super overheated when it's hot outside.
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Many of the cheap ones seem to be just a cloth that you soak, but idk if that's enough. I was thinking on putting little pockets in the sides to put in some little ice packs. Does this sound like something that would work?
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I think part of it might be because she was a stray all through winter as a puppy, so maybe her body got used to the cold? It was a frigid winter here.
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My dorky doggo:

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