Re: cold mornings...
List what you have done to you car. Off the top of my head it could be a million problems but start simple. If its been awhile since you have done the basics(filters, fluids, plugs, belts etc) that would be a good place to start and could solve a few issues, prevent more or at least narrow it down). If you have upgraded your intake and/or exhaust, mixed with cold air you can end up running too lean to the point where it will die until the engine warms up enough to get warm enough air to level out the mixture.
98 Camaro Z28/SS Clone, SLP lid, Throttle body spacer, Electric Exhaust cutout, Front strut bar, K&N Air filter, poly sway bar bushings, Full synthetic oil, Auto