If it was me I would lock up the trailer on the porch and cover it if possible. If it's a covered porch that will help to keep it from getting too iced up in a storm. I would bring the bike upstairs even if it is kind of difficult. Think of it as your daily gym workout. You are only riding 1.5 miles so you will need to do some additional exercise. The daily workout will save you the time going to the gym since you are a busy college student. It will continue working better and it will be easier to fix any problems if it is in your apartment and warm. If it's outside you will forget about it and then when it has a problem you won't know until it's too late to fix it easily.

Best way to carry a bike like this is to grab one hand on the steering stem and one near the seat post and military press it to about chest height. You can steer the handlebars around objects this way. Put it down and rest a couple of times if you have to go up multiple stairs.