Since this started happening recently - did you change anything recently? Install any new hardware? Any new software? Remove any hardware/software?
Another thing to check is your bios battery. If the bios battery is dead, when you power off the bios memory might be getting cleared, causing it to do some additional checks. Rebooting or hibernating might preserve the settings which is why it boots up quicker. This depends on if the splash screen is the windows splash screen, or the bios splash screen. If its the windows splash screen, then it's probably not the bios since by the time you see that screen, your past the bios checks.
another thing to check would be to boot into safe mode and see if that makes a difference. Turn the pc off - then power it back up and hold F8 just before you get to the windows splash screen. Select the safe boot option (with or without network). If that works, then you know the slow down is most likely due to some software running in the background - in other words it's not something critical to running windows.
If it boots ok in safe mode, then you need to start narrowing down the cause of the slow down. You can do that by clicking on the start button and typing msconfig. Run that.
Look through the services and the startup tab. There will probably be plenty in there you aren't sure of. The ones you are sure of, that you don't need or that you think might be causing the slowdown - uncheck those. Click ok, reboot - and see if the problem persists.
Since this only happens on a cold boot, i'm thinking it has to be something that runs close to the hardware - meaning something that monitors the hardware/runs a disk scan etc etc something like that. It seems unlikely it's software since whatever happens during a cold boot, should also happen during a reboot. The only main difference is the bios. So that's where i'd look first.
Quickest way to check if your bios battery has gone dead - power down the machine. Wait a few seconds for everything to spin down, then power it back on and press F2 or F12 or DEL - it should say on the screen what button you need to press to go into the bios setup. Go into the setup and look for the time and date settings. If those are way off - then your battery is probably dead. On many mother boards you can replace the bios battery. Some of them the battery is soldered on. In which case - you either have to be comfortable unsoldering it, or get a replacement mobo or deal with the slow down.