well it would help if you made the model of saw known right off the bat.
is the little foam 'filter' still in the plastic holder in the tank?
if the saw is pumping oil, i'd leave it so long as it wasn't emptying the tank out before running out of gas. most times people have the reverse problem with those saws.
thicker (summer grade) oil will help a little. might want to check the tank vent under the carb area to make sure it isn't plugged. there should be a cotter pin or a piece of wire in the hole, nothing else.
you should also make sure the bar is getting the oil and it isn't just coming off and down the back of it.