I have traveled to WDW during the January - February time frame three times. This is what I have learned:
1. Don't worry about the marathon. When we went (I didn't know about the marathon until it was too late to change the dates of our trip), we only noticed a few small things. Some of the bus routes were changed; the walkway from DHS to the BW area was closed; and there were no crowd problems. Most of the marathon takes place before park hours.
2. Evidently I am a poor planner because I didn't know that Presidents Day was a problem until a couple of weeks before our trip. I joined TourGuideMike.com and he gave us a good idea about which parks to avoid on each day. It really helped; we avoided all of the crowds and had a great time. MLK day will probably work the same. The only problem that you may encounter is that the hotels fill up fast so reserve your rooms early if they fall during this time period.
3. Check the weather frequently and pack both winter clothes and summer clothes. Most days the weather is perfect during this time: high 75, low 60. But we have had a few cold days during our trips and one was miserably cold because of the wind and the humidity. Be prepared for the occasional cold day. That said, most days my children wore shorts and could have swum if they wanted.
It is one of our favorite times to travel. Nice weather, for the most part, and low crowds. Don't forget that the first two weeks of December are nice too.
Regina