Hundesteuer is a municipal tax, set by each town or city's own Hundesteuersatzung rather than by federal or even state law, and it applies to keeping a dog over a certain age (commonly three months) within that municipality. It's a long-established, genuinely German quirk — no other country in this guide taxes dog ownership this way — but it's aimed squarely at residents who keep a dog in a particular town, not at someone passing through.
Dresden's own published Hundesteuersatzung is a useful real example of how these work: liability generally arises from keeping a dog in the city as of 1 January each year, or from the month after a dog arrives or turns three months old, with the tax year running on quarterly instalments. Its own visitor exemption only applies when all three conditions are met at once — a stay of no more than two months, the dog already owned on arrival, and dog tax already being paid in another German municipality — and each town's satzung sets its own version of this kind of rule.
For an ordinary multi-day or multi-week holiday with a dog, this tax essentially doesn't come into play: it's structured around dogs being kept somewhere, not around a short stay, and the mechanism that would make it relevant — actually registering residency or an extended stay of months — is a different situation from a normal trip. It's worth knowing the word Hundesteuer exists mainly so an unrelated mention of it doesn't cause unnecessary worry.

