Sweden's hotel sector doesn't operate under one nationwide pet policy, and whether a given hotel accepts dogs, what it charges, and whether there's a size or number limit is set by the individual chain or property. Many mid-range and larger Scandinavian hotel chains do accept pets as a matter of course, often with a flat per-stay fee, while smaller independent or boutique hotels vary considerably.
As with most of Europe, a hotel's pet policy is usually stated on its own booking page or listing rather than being standardised, so it's worth checking directly rather than assuming. Ask specifically about which rooms or floors allow pets, any weight or breed restriction, and whether the fee is per night or a flat per-stay charge.
A hotel admitting pets will generally still keep them out of breakfast and restaurant areas and away from pool and spa facilities, which is standard practice across most of Scandinavia and worth factoring in if those amenities matter to your stay.

