No, that shouldn`t have caused a seizure in warm weathrer when there is no winter or cold shutter. The seizure must have a other reason for example old fuel or an air leak somewhere.
You could may be get a problem with a seizure when you use the saw in warm weather and your cold shutter is closed in the winter position. In this case it is possible to get a seizure of the piston and cylinder, because the engine gets to hot. This cold shutter should prevent carburetor icing in the temp range near 32°F and high humidity.
That`s just my opinion.