Summer — June through August — is the prime season. The puffins are nesting at Hafnarholmi from late April and leave by August; the midnight sun keeps the sky bright all night; and glacier hike conditions on Vatnajökull are at their best. Late June brings the Humarhátíð, the annual Lobster Festival, when the town celebrates its langoustine catch with outdoor grilling, music, and a general sense of self-congratulation that is entirely deserved. If you can time your visit to coincide, do.
September and October offer a different kind of reward. The summer crowds thin out, the landscape turns russet and gold, and the aurora borealis starts appearing on clear nights — Höfn's low light pollution makes it an excellent spot for northern lights viewing. The weather is less reliable and some tour operators wind down for the season, but the Ring Road remains open and the glacier is still accessible.
Winter (November to March) is the ice cave season. The caves that form inside Vatnajökull are only safely accessible when the ice is frozen solid, and the guides running these trips know exactly when conditions are right. Driving the Ring Road to Höfn in winter requires care — the road can ice up and the coastal stretches east of town are exposed to Atlantic storms — but the reward is an Iceland that most visitors never see.