Who can see my hotmail display pictues in messages?

So i recently started to sell things on ebay as well as Craigslist. when people mail me can they see my display picture? i also send may to people on craigs list when im interested in buying something as well... i find it very impersonal when they are able to see it. its of my children and i just dont feel safe leaving my hotmail picture up there. i have no accounts linked so im just wondering when we mail back and forth can they see it?