Davos: CHF 5.90 per person per night. The page lists a single standard rate, with no accommodation-category or seasonal tiers; it also states that the listed amounts are subject to change without notice.
Children under 12 receive a 50% reduction. The page otherwise says the charge applies to all visitors; it does not list any additional exemptions.
No canton-wide day cap found; register with Davos Klosters Tourismus