Hörður began his senior team career at the age of 15 with Fjölnir Reykjavík.

At 17, he moved to Spain to play for Gran Canaria, but returned shortly later to Iceland and joined Njarðvík.

On 17 June 2013 it was announced that Hörður made use of the option to buy out of his existing contract for a four-figure sum.

Due to the Eurobasket 2013 and the related absence of some players in the Spanish first division, Hörður played with Bilbao Basket for the preseason.

[12] On 12 April 2017, the day after being eliminated with Keflavík from the Icelandic semi-finals, he signed with Bondi Ferrara of the Italian Serie A2 Basket.

[14][15] In December 2017, Hörður left the club and expected to sign back with Keflavík.

[17] On 29 March 2018, after Keflavík had been eliminated from the Úrvalsdeild playoffs, Hörður signed with Kymis of the Greek Basket League.

[24] Hörður was a part of the first Icelandic national basketball team to qualify for a EuroBasket tournament, in 2015.