Luckily for Rose, Swift offered a helping hand, taking the jacket off the award-winner as she took to the microphone to speak.
Rose thanked "the most beautiful jacket holder in the world" in a heartfelt post on Instagram.
"The true story of how one 'sometimes girl' ( me ) was surprised and brought to tears by a surprise 'always amazing and giving' girl @taylorswift," she captioned a collage of images.
"No I can't believe the passing of the coat was caught so magically.. 'Are you sure Taylor?'.. 'I don't know.. I am really hot but also I don't think I can have you hold my coat."'
Rose later thanked her fans and Swift for the award saying she felt honoured by the experience.
"Tonight was EVERYTHING... Thank you @taylorswift thank you @glaad thank you to everyone who came out to be part of an amazing night. I feel truly blessed and humbled. I'm going to go cry and hold my pillow like a teddy now because I feel like I'm dreaming," Rose wrote.
The honourary award has previously been presented to stars including Laverne Cox, Wanda Sykes, Alan Ball, Ellen DeGeneres, and Sir Ian McKellen.
Rose wasn't the only star to be presented with an award, the night also saw pop-star Demi Lovato honoured with the Vanguard Award, presented to media professionals who have made a difference in promoting equality.
The 23-year-old star was handed her award by friend and tour mate Nick Jonas, who also took to social media, writing, "I was so humbled and honoured to be in that room tonight with so many incredible people from the LGBT community... This was one of my proudest moments as her friend. To see the lives she's touched and how she is constantly true to who she is."
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Other GLAAD Media Awards winners included Bessie (Outstanding TV Movie or Limited Series), Carol (Outstanding Film), Transparent (Outstanding Comedy Series), and Ricky Martin (Outstanding Spanish-Language Music Artist).