A tiny tug
Goosebumps happen when tiny muscles at the base of hair follicles contract, lifting the hairs and making small bumps in the skin. Cold or strong emotions can trigger this automatic response.
An open window and a favourite song can therefore produce surprisingly similar-looking arms. You have not suddenly grown feathers: your existing hairs have had a little lift.
A coat from the past
These muscles are called arrector pili. The US National Institutes of Health explains that pulling hairs upright helps animals with thick fur stay warm.
Humans have much less body hair, so the same response does not give us a useful furry coat. A warming trick for a thick coat looks rather less useful on a nearly bare arm. Your jumper still has work to do.
When a song raises your hairs
Cold is not the only cue. Cleveland Clinic describes goosebumps brought on by fear, excitement and experiences such as music or films.
That is why an unexpected chorus can leave you with bumpy arms in a perfectly warm room. You did not decide to raise each hair: the response happens automatically.
Same tiny muscles, different moment. Apparently your skin has opinions about the chorus.