The idle control (IAC) seems to have a problem. That bike should always idle good, even at 30 degrees. Maybe it's stuck inside, or someone may have plugged the air hose somewhere. It's a little rotary valve that opens when cool or cold. Then, upon starting it gets 12v to start a heater warming up internally, and also, uses water circulation to also aid in a faster heating of the bi-metallic coil inside. That levers said rotary valve, causing it to start closing the air passage off. They do stick, and/or get gummy inside.
Upon starting, the idle typically will go to about 12-2500 rpm, and slowly head towards the idle screw setting as the engine warms up. Works very well, when working right. Better than the 1800, in my opinion.
Get a manual. Then, find the LTD/SEi supplemental. The air valve is inside that part of the manual.
Dennis is right. That 1200 needs revs. They're gut-less at real slow engine speeds. It likes revs. Not like the 1500 or 1800. Those are more like old Deere engines, stump pulling power at low rpm.
I always ran my LTD at 1050 idle, and that kept the alternator charging just fine, also. (Nippondenso) I always started the bike in gear, to prevent ugly noises when shifting into gear with the bike cool or cold. I rarely let it warm up. Just take off like a sane man, and take it easy till a bar or 2 on temp gauge.
This reply is assuming that the tune is ok. There could be other issues, which would compound the problem. Like, throttle body balance, ignition condition, fuel pressure, vacuum hose problems, etc.