Does high arched palate cause snoring?

Snoring: Many causes. Can be from growths on turbinates in nose or more simply from the relaxation of the soft palate blocking the airway. See your ent.

Yes it does: A high palatal vault may cause snoring, sleep apnea, tooth malposition and lip incompetency (no mouth seal). I a study done with 1065 children they found out children with high vaults has enlarged tonsils and 80 % of them had allergies.

Yes: Sine the roof of your mouth is the floor of your nose. High palatal arch cause narrow the airway and breathing from nose.