Really need more information. Are you looking just to remove the screens and replace them with something to block the elements or are you planning to turn the porch into living space for the winter. Not practical to try to winterize a porch and leave screens in place open to the weather.
Do you mean winterize and turn it into an enclosed porch? If so, it depends on how sturdy the structure is. You might need new windows that don't leak, for example. You'll need a heating source. You also need insulation in the walls and ceiling and perhaps the floor. I would talk to a contractor and a heating and cooling company. Also check with city hall about whether you need a variance (sometimes if it's now counted as indoor living space you do).
If you just mean sealing it off, check to see if there are storm windows to put in. Otherwise plastic can do, although it doesn't always look great.
Here's a fun read on someone restoring a porch-- hopefully yours will be much easier.
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