Nuzzle

[Becky]

To go with head poised like a swine, with nose down.

[Marquetta]

Rub or push against gently with the nose and mouth.

[Tanya Shivari]

To [cuddle] against another person or [object] close with head and or [shoulders].

[Sommer]

to touch, rub, or press something or someone gently and/or in a way that shows your love, especially with the head or nose, usually with small repeated movements: