I'm in southern virginia with similar climate and have noticed the same clunk starting a few weeks ago after cooler nights in my 2009. It always goes away after about 10 mins of driving. My intitial forum research a few weeks ago made me believe an entire front-end suspension refurbishment was necessary. I'm not excited to take that on with my limited experience. But after seeing your question and more googling yesterday, I think just replacing the sway bar bushing will fix it.
I haven't put my eyes or hands on the actual bushing yet, but I did find a promising post online where someone replaced the bushing without loosening the crossmember. They described replacing the part only by feel reaching over the crossmember using just the right combination of sockets, extensions to reach the bolt and ratchets to have enough torque. I think I read you have to watch out for a brake line or some other interference on the drivers side. And they mentioned you can only reach it from gettin under the midsection of the car.. I guess scooting under the drivers door. Another thing that helps is find the drawing up the assembly on jimellismazdaparts.
Although an aftermarket bushing would probably be better I'm gonna go to mazda today and pick up the oem ones. Maybe the redsigned 2010 part fits mine.. and hopefully they bring up the TSB. Let me know how the job goes for you. If I get to it first I'll give you some lessons learned.