Learn French: En été, je mets un short. - In summer, I put on shorts.

In French, a pair of shorts is treated as a single item of clothing, so it is singular: un short. English uses the plural for many leg-coverings (pants, trousers, shorts), but French generally uses the singular for them, just like un pantalon for a pair of pants.

Why do we say en été instead of using another preposition like dans or à?

French uses the preposition en for seasons that start with a vowel. This covers summer (en été), winter (en hiver), and autumn (en automne). The only exception is spring, which uses au (au printemps).

Could I use the verb porter here instead of mettre?

You could, but it changes the meaning slightly. Mettre (here conjugated as mets) focuses on the physical action of getting dressed, just like "to put on" in English. Porter means "to wear", describing the state of having the clothes already on your body.