The -te form can be used to make a compound verb showing that both verbs happen together.
帽子をかぶってハイキングしたほうが温かいです。
It’s warmer to go hiking with a hat on.
How to deal with negatives
Remember that there are two ways to make the -te form of a negative verbs: -ないで, and なくて.
When making compound verbs, it’s more common to use the -ないで form
メガネをかけないで泳ぐ。
I swim without my glasses on.