We have been on MLK weekend in 2008-2009 and 2010.
The touring groups were not a problem. There were there in 2009, but overall they were not that much of a nuisance.
Corwds tend to be a littler higher on teh Sunday b4 MLK day and on MLK day---but---it was still not "crowded"---very manageable wait times-
Not sure about discounts---we are DVC members---so the discounts done help us much.
As for weather, we have had some COLD days in 2009 and 2010. But, the crowds were so low, the weather did not bother us too much. When it was cold, we did looong lunches or relaxed at the resort. There is so much to do and see at WDW, that 50 degree weather isnot tht big of a deal to me---see some shows, try a restaurnat, etc...
Hope you guys have fun...