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I'm happy that you have asked me to assist you with your child and hope that you can benefit from my many years of helping parents like you. Yes, since when they have fever the body may send the wrong signals to the blood vessels causing them to constrict and thus less blood flows to the extremities. More important is the cause of the fever so I would be more concerned about sore throat, cough, etc. and how long the fever has gone on.
Eventually the blood vessels dilate as the skin is the best source for radiating heat away from the body and then they sweat.
Depending also on the age of the child, the thermoregulatory mechanisms are less refined the younger the age of the child so cold hands and feet can be pretty common in infants and young children even when they are otherwise well.
Please let me know if you have further concerns or questions as I'm about to leave for my after-hours clinic but will be online there after 4 PM Central time.
Thank you. She is 3 and typically has very hot feet and hands when she has fever. I was concerned this time because the hands and feet were very cold. The pediatrician at the office (not our usual ped) said it was common, but it's hard not to be concerned when the internet only returns things like Meningitis. :)