I also own a GSP and I would only bring her if the weather is mild. They just are not made for the cold. The unique advantage of the short coat is they don't heat up as bad as other dogs in mild temps while chasing quail and pheasant, and they are very clean.
Unfortunately, this works against them in the cold because their light bodies and short coat doesn't hold the heat. I take my dog with me everywhere I go, but when it gets cold, I don't take her waterfowl hunting where she is required to sit still.
Other than that, they are smart enough to pick up on any training you provide. Start with bumpers and work your way up to the real thing.
If your GSP is anything like mine, you mostly just need to avoid screwing up the natural talent *** gave them.
We owned a GSP for eight years and took her duck and goose, phesant , quial , prarie chicken , sharp tail grouse, all in the same day for 3 seasons and she never gave up. It didn't matter how cold it was if they have the drive and want to hunt they will do it. Just bring them in at night and get them warmed up. She would retreve in ice water with snow and always right to hand.
She would retreve geese as big as she was. GSP are bred for an all around hunting dog if you get a good blood line.
I have a GSP that I break ice with to retrieve ducks. If you get a versatile dog from a good breeder and then learn what it is going to take to get the dog to the level that you want then you will have no problem. If you think you are going to be doing a lot of cold weather hunting I would suggest looking at a dog with a longer coat and more suited for cold weather water retrieves.
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