I think creating a Google profile fixes this. Google Profiles are now replaced by Google+ profiles, but as before, I think Google still takes the Google profile image of every user.
So, if you create a Google+ profile with the same Google account as you have your YouTube account with (probably just your Hotmail address) and upload a different profile picture to that profile, that picture will show up to Gmail users.
EDIT: You asked why this is so. Well,
Google uses your Google Profile as the identity of your Google Account. Your Google Account is used across all the Google products that you use. But it's also used to represent you to other Google users. Google+ profiles are the primary source for Google to create your identity but if you don't have one, they will take another identity they do have from you, f.e. your YouTube account.
Also, Google wants to show Gmail users more than only an e-mail address. If Google can link that address to a profile they have, they will show that (public) identity to users interacting with that address.
So basicaly, Google creates central identities for their users, which are combined from all their accounts on their services and uses these identities to identify you to all other users from all Google services.
Besides, Your Google+ profile just let's you define you identity inside Google's system. Google+ is in fact the social and identification layer to every Google product, so it's more than just a social network. You don't have to worry you won't use Google+ actively, just use it to define your identity.