(covers information from several alternate timelines)
T'Pol and Archer sharing a blanket
A blanket was a piece of fabric used to cover an individual while sleeping. It could also be used to provide warmth.
While being held hostage by a commando of the Andorian Imperial Guard in the meditation room of a Vulcan monastery at P'Jem in June of 2151, Captain Jonathan Archer offered Sub-commander T'Pol to share his blanket with her during night. She first rejected his offer and told him that the cold was preferable to the smell of a Human and it was over twenty-four hours ago since she used her nasal numbing agent. However, she later accepted and shared the blanket with Archer. (ENT: "The Andorian Incident")
A blanket used for coverage at the catwalk
The crew of Enterprise NX-01 and the Takret Rellus Tagrim, Renth, and Guri used blankets to separate the compartments at the catwalk for privacy. (ENT: "The Catwalk")
In 2233 of the alternate reality, baby James T. Kirk was wrapped in a receiving blanket before being handed to his mother. (Star Trek)
In 2364, an injured Beverly Crusher asked Jean-Luc Picard if he'd brought a blanket with him to Minos. (TNG: "The Arsenal of Freedom")
In 2367, Susanna Leijten compared her feeling of mental lethargy to having her brain "wrapped up in a blanket". (TNG: "Identity Crisis")
Gentry covered with a blanket
The Doctor covered the dead remains of "David Gentry" with a blanket when he performed a post mortem analysis in sickbay. (VOY: "In the Flesh")
In 2373, while The Doctor's holographic daughter Belle was dying, her brother Jeffrey brought her a blanket. (VOY: "Real Life")
In 2378, Seven of Nine received a blanket from a Ventu girl living on Ledos. When she got lost looking for the remains of a class 2 shuttle in a forest and got cold, the Ventu girl gave the blanket to her to warm her up. Later on board USS Voyager, Commander Chakotay gave it back to Seven. (VOY: "Natural Law")