I think...yes...you now will have different microbes predominating. Different food source and cooler temperatures. Slower overall due to low temps--but --high moisture is a slight help.
Years ago there were a couple products on the market called "Compost starters" or something similar. Contained bacteria and fungi a a powder that would break down the grass clippings and leaves either in the lawn or in an actual compost heap--that is--if you believe the advertising and promotional material. I didn't notice any difference...but...if anyone knows of a product that actually works...I would be interested.