Hello everyone. I have been a boxster owner for only about 4-5 months. As winter approaches, I need to make some changes and I have come seeking advice! (Surprise surprise

)
Background
My boxster (01 tip) has been a florida car all its life. The car was originally purchased in FL, spent its full life there, and was bought used by me there as well. As a result, this car has never seen a winter and needs to be prepared. What steps would you advise I take to prepare?
My tentative plan is to go to my local Pcar dealership and ask them to "winterize me". However, I would like to have an idea of what I need to do in advance so that I do not get conned into something useless and so that I can make sure they do not omit any critical changes.
I also plan on driving the car in the winter (no garage - and I live in upstate NY

will this be an issue?). I will not drive it in heavy snow and will try to wait a few days after major snowfall to reduce exposure to salt. Because of this plan, I will stick with all season tires. However, from a mechanical standpoint I must be ready!
Also on an unrelated note,

when I started my car up this morning, the engine did something very troubling! It shook/vibrated back and forth a lot - it felt almost as if it were an MT car and you were trying to go from a stop directly into 3rd gear. What would a possible cause be and could this be a big issue? No CEL, humidity that morning was incredibly foggy and cool. After she warmed up, all was swell.