There's a little-known, but widely accepted, method of literary characterization here dubbed "anthropodwarfism." It goes like this: If [insert name here] were one of the seven dwarves, which would she/he be? (Note: do not employ this method in any formal, academic, or public forum. Ever.)
Rabbit would be Grumpy. Hands down. Milne introduces us to him when Pooh goes to visit: "'Is anybody home?' called out Pooh very loudly. […] 'No!' said a voice; and then added, 'you needn't shout so loud. I heard you quite well the first time.'" (Winnie-the-Pooh.2.8-9.). So there you have it. Rabbit is not exactly welcoming. He devises intricate plans to get rid of Tigger, and Kanga and Roo.
Speaking of his plans, Rabbit, it turns out, is a go-getter. The action in chapter five kicks off with "It was going to be one of Rabbit's busy days. As soon as he woke up he felt important, as if everything depended upon him" (House.5.1). And Milne describes him for us, "Rabbit, who never let things come to him, but always went and fetched them" (House.5.55).
But Rabbit certainly has a softer side. He plays Poohsticks with the best of 'em, and ends up being great friends with all the people he tries to oust in the first place. Remember when he tried to intimidate Kanga and Roo? Turns out, Roo is the first one he thinks to visit on his important day. And don't forget that Rabbit leads the charge in finding a new house for Owl.