I am thinking of piping outside air to my furnace. What could be the adverse results?

You can do that but the only thing is that will make it harder for the unit to condition the air rather then circulating the conditioned air in your house youll be mixing in hot or cold air into it. It is fine to do just be sure its not near any vents and it is screened to keep out pests and nests. Make sure rain water cannot enter and cause any damage to ductwork.

Unless its designed to run on partial fresh air that would be a mistake. If you wish to use fresh air for the products of combustion that would be absolutely fine. Do make sure the pipe has a fine screen on both ends. The air being heated & cooled is designed to be recirculated.

Put in a heat ERV (energy recovery ventilater). You exhaust air and bring in fresh air and transfer BTUS to the fresh air, taking some load of of the furnace.

If you bring in outside air then you must also vent the same amount of air back outside. If you don't do this then you will be trying to pressurize the house and you won't have as much warm air flowing because you aren't exhausting any of it.

No filtration and higher energy bills. Possibility of insects, mice, etc entering the house that way.