In Twin Peaks Agent Cooper had a pretty open mind, including following leads from dreams, throwing rocks at bottles to work out who was a suspect, etc. So why was the Log Lady so hostile towards him?
The Log Lady typically has a pretty sour disposition regardless of whom she's talking to. In Episode 5, Cooper's Dreams, she doesn't seem happy to see Cooper, Truman, Hawk, or Hayward.
But she bears a grudge against Cooper from the moment they meet, and it's precisely because Cooper fails to be open-minded. From this transcript:
As COOPER eats his pie, the LOG LADY comes up to them as she passes. LOG LADY For your information, I heard you speaking about Laura Palmer? COOPER Yes? LOG LADY One day my log will have something to say about this. My Log saw something that night. COOPER Really? What did it see? She holds the log out. LOG LADY Ask it. A moment of silence. COOPER, unsure what to do, peers down at the log. Disappointed by his lack of action the LOG LADY counters ... LOG LADY I thought so.
He can't bring himself to talk to the log, and the Log Lady writes him off as just as narrow-minded as the rest of the town. Cooper is a sensitive, spiritual guy, even a little psychic, but his personal brand of weirdness hasn't fully prepared him for what he finds in Twin Peaks. I saw him initially as a kind of knight in shining armor, who defeated evil and dispelled mystery simply by showing up, but the more I think about the show (and the more I watch it) I realize he's more complicated and more flawed than that.
In addition to Ryan's great answer I want to stress the fact that she possessed a information that could be of use to Cooper and the rest of the team. When they arrived at her house she said they were 2 days late. They most likely forgot her invitation and didn't give much thought to her given her unusual behaviour.
I believe that excluding her and not believing she has anything to contribute led to her remarks against agent Cooper.