He originally started competing as an alpine skier after his family moved to Alaska when he was five years old; however, he subsequently switched to snowboarding and cross-country skiing.

After moving to Aberdeenshire at the age of 11, he started to focus on cross-country skiing on a serious basis alongside friends Andrew Young and Callum Smith.

Musgrave scored his first World Cup points in the 3.75 km prologue race of the 2011–12 Tour de Ski on 29 December 2011 in Oberhof, where he finished 28th.

He equalled this result on the 25 km freestyle pursuit stage of the 2015 Tour de Ski in Toblach, setting the fastest time of the day.

[8] At the 2014 Winter Olympics, Musgrave qualified in 27th place in the individual sprint, the best-ever performance by a British cross-country skier, but failed to progress from his quarter-final.

[10] After the Games, Musgrave backed up his victory in the freestyle sprint at the Norwegian championships earlier in the season to win the overall national title.