Not a problem now....but...

So this past winter when my car was still undergoing restoration, It started very hard. It had probly twice as much oil in it as it was supposed to have. We changed the oil and about 2 weeks later it started running good. But it started great when we first got it, and it only started not starting when it got cold. It had under a 1/4 tank of gas. Could it have been the fuel pump? We never did anything besides change all the fluids.