You can definitely install a newer version of Android on there. The latest is Ice Cream Sandwich (ICS). I honestly don't know how smooth it will run on the HD2 (I own an Evo myself). Do you know how you are running Android? I helped a friend of mine install the "prj Clean Desire" ROM on his phone into nand. This means that when you boot up it runs Android directly out of the phone's memory. Apparently you can also dual boot (by running something called like haret.exe?) and then run from the sdcard.
Note that installing a new ROM is going to wipe EVERYTHING on the phone, so you will want to backup your contacts (unless they are already all stored in your google account), backup SMS (if you want them), etc.
If you have nand Android then you should have MAGLDR installed on your phone. Simply power it down, then press and hold the power button. If MAGLDR is installed it will load up into a black screen with white font that says MAGLDR at the top. From here you can just select the "USB Flasher" option, connect to a computer via USB, and then flash over a new ROM. Most of them are just a simple .exe file that guides you through the process.
You can always flash ROMs from ClockworkMod recovery, assuming that is installed on your phone. You can get to this by first booting into MAGLDR and then selecting the recovery option. I seem to remember there were 2 options that said something about recovery in MAGLDR, though I don't remember which one to select.
If you're wondering what ROM to get, just do some google searches for something like "htc hd2 ics". I'm not sure if there are any 100% working ICS ROMs, so if you want to try gingerbread you can always google for that instead.
Here is an ICS ROM that looks promising. It says the only thing that doesn't work is native USB tethering (though wireless tethering does):
[9.Mar.2012] NexusHD2-ICS-4.0.3-CM9 V1.5 - xda-developers
Any further questions just ask and I can try to help.