Cuddle up often means seeking comfort in a cold or unwelcoming environment.

Seeking Warmth

Cuddle up implies being in very close physical contact with something or someone.

Physical Proximity

Cuddle up doesn't always require another person; one can cuddle up with objects too.

Cuddle up used in this way is a public or intimate showing of affection for someone.

To cuddle up to someone emphasizes seeking comfort or reassurance from their presence.

This usage often serves to provide physical reassurance in times of sadness or fear.