Again, as folks have said, if you're not comfortable then don't go.
But I'd go, personally. Cruising at 3,000' you should be in good shape to make this happen, and remember if you start to pick up ice for some reason, you can ALWAYS drop below that to shed it. As long as you have some decent temps below you to get rid of that ice, you'll *probably* be ok.
What would my big concerns be with this flight? Icing, obviously; but that can be avoided by not going into the clouds. If you have above freezing temps below you, that should nullify that threat pretty well, as the area of the country you're going over is nothing but farm land. Figure out where the towers are and make a backup plan to be able to get down to MVA or lower if you need. I would watch temps VERY closely, though.
I'd be concerned about being able to put the plane down somewhere if you have an engine failure, especially from that altitude. In fact I'd probably be MORE worried about that than the icing issue (again, as long as you have above freezing temps below your altitude).
Other issues are any emergencies that could pop up during a night IFR flight in a single engine aircraft. A busted alternator is going to require quick work on your part if you end up in IMC, and you'll have to act accordingly if something like this happens, performing decisively and with purpose.
When it comes down to it every flight has an amount of risk. Heck sitting on the internets has a very high proability of causing an anurism. That being said, we continue to live our lives and mitigate risk as much as possible for the given conditions. That is your goal as a pilot; to mitigate risk. You can't eliminate it, but you can do things that will lessen its effect on your flight.
The decision is yours and yours alone as PIC. Lots of folks bag on flight instructors tooling around in single engine aircraft and how it doesn't help you later in your career. The things you're dealing with now, and these issues that you'll deal with later as a flight instructor are incredibly similar to the situations you'll run into on the line at a freight company or regional airline. You are there to mitigate risk, and you use the tools you have at your disposal to make sure that you do that. The only difference is that your tools are different. I.E. If look at that while driving an RJ for a few seconds and go back to my paper. I look at that while driving a Chieftain and think to myself, "Cruise at 8,000', watch for ice, get ready to climb, go back to my paper." I look at that in a 172 and I think, "Stay below the clouds if possible, avoid icing, be very decisive in my handling of the situation."
Zap himself will be there so this trip is of fairly high importance.
