Since I have been home for winter break (dry, cold midwest) I've had a hard time working out/breathing?

Hydrate & humidify. It may be as simple as staying better hydrated and also consider increasing the humidity in at least the room you are sleeping else the entire house via a household system.
Asthma. Exercise induced asthma affects people who don’t have other asthma symptoms. They are more sensitive to temperature and humidity of the air. Cold dry air inhaled through the mouth reacts with warm moist air in the lungs triggering an attack. Breathing through the nose warms & humidifies air which helps. Its hard to breathe through your nose when exercising but a face mask/scarf may help.