Both options, "forget to wear" and "forget wearing," can be grammatically correct but have slightly different nuances.
Explanation:
"Forget to wear":
This emphasizes that you forgot the action of putting on gloves. It focuses on the failure to complete a future or intended action.
Example: "When I forget to wear my gloves in cold weather, she takes hers off and puts them on my hands."
This is the most natural choice in this context, as it aligns with the idea of forgetting to do something important beforehand.
"Forget wearing":
This would mean you forgot that you were wearing gloves at some point (a past action). This phrasing is less likely to fit the intended meaning here.
Example: "When I forget wearing my gloves..." would imply you forgot that you had gloves on at some point in the past, which doesn't match the scenario.
Recommendation:
Use "forget to wear" for clarity and to match the context of the sentence.
Corrected sentence:
"My friend Amy is warm-hearted. When I forget to wear my gloves in cold weather, she takes hers off and puts them on my hands."