if you use the connector, the list should sync up, not down but Hotmail doesn't use DL's, it uses categories instead.
From
http://www.slipstick.com/emo/2009/up090528.htm#4
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What Hotmail/Live calls "Categories", Outlook knows as Distribution lists. The connector will sync the "category" into Outlook as a distribution list name but it does not sync the members, leaving you with an empty distribution list. Importing DLs has always been buggy and members rarely made it through the import so this comes as no surprise.
Distribution lists created in Outlook will correctly sync to the Live account, adding the DL members to your online contacts if the contact does not exist, and creating the "Category" containing those addresses.
Solution: Create distribution lists in Outlook and let the connector sync them to the server.
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