Yes, the cold will make it possible for your eyes to get crusty. Since you have the cold, your immune system will be decreased. The whole body will work slowly at every organic part. And the eyes may easily get the bacterium if you don't care about them. Thus the bacterium will cause the crusty eyes. You should use some medical treatments to make them get well.
Crusty eyes in the morning commonly happen to children and adults. There are a lot of things that can cause crusty eyes, including cold, allergies, infections like blepharitis, conjunctivitis and corneal ulcers. See a doctor to confirm what casued your crusty eyes and have a treatment to avoid it becoming worse.
Yes, it is possible to get crusty eyes from cold. When you catch a cold, the immunity function of human body impairs, thus the zymad is liable to intrude human body through dust or other substances, which can make you get crusty eyes. Furthermore, viral common cold is prone to give rise to bacterial infection, which causes crusty eyes. Under such circumstances, you need to form a good personal hygiene habit such as washing your hands frequently and have an adequate sleep and drink more water to keep fit. Keep the room well ventilated and do not go to crowded places as far as possible. Wash your fittings or ornaments with great contains of fiber such as bedding, mattress and carpet at regular intervals to avoid virtue hiding in them.