'seeming'みたい is a part of みたいだ, which is derived from 見たようだ according to 大辞林(daijirin).
Need to check up on the difference between みたい and よう usage.
Don't confuse みたい (seeming) with みたい (wanting to see). The latter is the たい (tai) desirative form of みる (I'm not sure how 'seeming' みたい was derived)
The first time I came across みたい in that form (the example) I processed it from the literal meaning "I want to see that he has a cold" -> "I want to say he has a cold" -> (oh!) "Seems like he has a cold" . . . Ok, it's a stretch but well these are the things you do when you have no one to ask.
There are certain nuance changes in みたい as my added examples show.