I've been commuting for about a year and ride also in the rain if I have to but not often. I noticed my headset makes a cracking noise if I lift the bike up at the front and turn the bars from side to side about 60 degrees or more each way. There's no noise if I just turn a little bit. I read on Sheldon Brown that the lower headset bearing gets a lot of grit into it if you ride in the wet.

Should I pull it apart and pack the bearings with new grease?

If you know how to do that, and have the tools, then the answer is absolutely yes.

Cheers.

I read somewhere this week that if your headset bearings make a cracking noise, there is too much preload. I just loosened the clamp screws on my steerer and then backed off the preload screw by 1/4 turn. There is a little bit less resistance to turning now, possibly (wasn't much resistance before I adjusted). Cracking noise is still there.

Threadless is so easy to service, needing only a 5mm hex key, that there's no reason not to check out your suspicions. In case your bike has a loose ball headset, raise the stem about 1/4", then keeping the fork up into the frame turn the bike over and lift the fork to look at the bearing. This way the cups will keep the balls in place. If the headset needs work, continue working upside down if it has loose balls, otherwise it doesn't matter and you can wok whichever way you're more comfortable.

When you put it together, consider putting a wide rubber band (cut inner tube, or a broccoli rubber band, Andy Boy is best) over the lower bearing to cover the gap. It won't make a seal, but is a very effective deflector or dirt and water kicked up by the front wheel.