Getting around Iceland and Scotland without a car, and with a rolling bag…

How stupid of an idea is this?

Planning a trip to Scotland with a multi day layover in Reykjavik at the end of the month. Because of the cold weather, I plan on packing quite heavily. I’m not an experienced winter weather driver, so I’d prefer to not rent a car (also - driving on opposite side of the road).

Is getting around without a car and with a rolling bag going to be painful? How good is public transport - and are roads paved or cobblestone in most areas?