Toyota as typical was very late to the game with fuel injection on the Corolla. This generation car tended to have a carbuertor. I am assuming you have the standard 1.8L engine with 138 hp that was carbuerated. If that is the case, it might be as simple as the air filter needs to be replaced. I am betting it has to do with the carbuerator. My first car was a used 1986 Toyota Corolla that was also carbuerator, and it was much worse as in cold weather the choke did not work well and it wanted to stall and hesitated badly until it warmed up. In that case, I had to rebuild the carbuerator and it was fine then.
With the minor conditions you are talking about (I am assuming this occurs nearly all the time) the air filter cleaning probabily will do it. If not, then it is something else regarding the carbuertor almost guaranteed. Good luck.