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1.
An insult / derogative term deriving from the video game Skyrim, often used by City Guards to suggest a person is weak and / or young / inexperienced.

Possible explanations:
Young babies drink milk from their mother's breasts.
and / or
Those who can't handle mead or ale instead drink milk.
and / or
Milk in Skyrim will restore a Warrior's resource for hard-hitting sword swings. Those who require Milk for this purpose would likely be lower-level, and inexperienced.
Don't be such a milk drinker.
by Dovahkiin & M'aiq the Liar December 22, 2011
 
2.
A baby, used as an insult. The insult seems to pre-date Skyrim, and may have origins in Scottish culture.
An old Scottish saying is:

"Bread and cheese is gude to eat when folk can get nae ither meat.
Bread and milk is bairns' meat: I wish them sorrow that be it."

Seems to refer to a "milk drinker".

Another Example: "What do you think of that, Mr. Pajama-Wearing, Basket-Face, Slipper-Wielding, Clype-Dreep-Bachle, Gether-Uping-Blate-Maw, Bleathering, Gomeril, Jessie, Oaf-Looking, Scooner, Nyaff, Plookie, Shan, Milk-Drinking, Soy-Faced Shilpit, Mim-Moothed, Sniveling, Worm-Eyed, Hotten-Blaugh, Vile-Stoochie, Cally-Breek-Tattie?"
by Pajama-Wearing Basket-Face January 09, 2013
 
3.
A weak or spineless person. The implication is that milk is a drink for children, whereas real men drink booze. Popularized by the Bethesda game Skyrim.
You really think you're a match for me, milk-drinker?
by Psycho Robot February 24, 2012
 
4.
A person who prescribes to chumpish behavior. Favorite activities include being vanilla, adding little value, thinking they add a lot of value. Love chivalry and being "just one of the guys" in the worst kind of way.
Check that kid sucking down 2%, classic milk drinker.
by nnkwfwef May 22, 2014
 
5.
1.A person of cowardly actions and deed. Usually lazy and unwilling to take action.

2.A pussy
1.Hah, Those europeans can be so cowardly sometimes, bunch of Milk-drinkers.

2. Heh, Those hippies are nothing but a whole bunch of cockholstering, bootlicking Milk-drinkers.
by 047loeonos May 25, 2012