bright eyed and bushy tailed: to look full of energy, healthy, well rested, and thus attractive. Like a fox - whose eyes are always bright and whose tail is always bushy.

blow/brush away the cobwebs: the cobwebs refer to the groggy, only half awake feeling one gets when one has just woken up - or if you've been inside for ages working or studying. Brushing them away means going to do something refreshing - often meaning to go outside into the fresh air and the wind - so as to feel more awake. If you are outside in a particularly strong wind you often say something like "well that really blew the cobwebs away."

A: "You're looking bright eyed and bushy tailed."
B: "Yeah, I feel great. I got lots of sleep last night, I think I needed it, and its just such a lovely day today. Clear blue skies, crisp air. Just right for a long walk."
A: "Let's go for a walk then. I don't feel as full of the joys of spring as you evidently do, I need something to brush away the cobwebs."
B: "OK, I'm up for anything this morning."