Thank you for your query.
You have mentioned that your son does not wear flannel or fleece and still he sweats a lot. You need to see if this is of recent onset or has been occuring from the beginning. In case it has been persisting for a long time then it has to be seen that he is not being overclothed compared to the environmental temperature. Feeling cold
by touch is not unusual when one is sweating as it is the body's mechanism to keep the body cool.
If the sweating persists despite reducing the clothing then it shall be better to consult your doctor.
I hope I have answered your query to your satisfaction.