It really depends on your water temperature not the outside temperature; both koi and goldfish act that way when the temp is low, also they go through a shock when you first get them and may take a couple of days to get adjusted. They say the first koi needs a minimum of 1000 gallons of water and each additional koi would need 250 gallons, this is for a full-grown koi.  The water quality must be pristine; and koi will develop nasty ulcerations if water quality isn't kept up.  Gold fish on the other hand can survive in much smaller ponds because they don't need the same water requirements.  There are some very beautiful goldfish that look exactly like koi except don't have the little barbs that looks like a mustache and they only grow to 10 –13.  We built a koi pond with all the proper filtration, but when I found out koi will eat the water plants, I switched to goldfish.  Koivet is a wonderful website that has lots of great information on koi and goldfish. 
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