Wait. You work in a freezer warehouse and you're worried about the cold?
On the peninsula the cold is not really a factor. Water, rain, sleet, and sea spray are the problems. Your camera should be fine. Maybe bring a plastic bag to keep it dry, in case you're going ashore in bad weather. During March expect temperatures between -5C to +5C, with wind, rain and snow.
If your asthma is under good control at home with medication, I wouldn't worry too much about it. Just be sure to bring meds, steroids, or whatever you normally use. I know several people with asthma who are currently working on the Peninsula and have had no problems, but you have to decide for yourself based on your own condition and history. If you need warmth you can always go back inside the ship.