Is it possible to make a normally warm area change to a normally cold area?

You could change the gravitational constant of the universe or smack the planet with a colossal meteor to alter Earth's orbital parameters... Or somehow start an ice age... Or completely fill the sky with volcanic ash blocking the warmth of the sun... Or turn off the heat...

But seriously, that's what we're doing while causing global warming. We just focus on the warming part, but there are parts of the planet that are cooling off as well.

Any change in the earth's orbital parameters would have a near equal effect on all of the earth even if it was altered into an elliptical orbit. In that case it would be very hot in the perigee of the orbit and very cold at the apogee but it would affect all of the earth the same.

Seasonal temperatures are caused by the 19 degree tilt in the earth. As it moves around the sun, in Winter the northern hemisphere is facing away from the sun and in Summer it faces towards the sun. If it were possible, increasing the angle of the tilt would increase the seasonal variation and making the angle more shallow would make temps more constant year round.

It would be very difficult if not impossible to control temps regionally or locally. The air around the earth is constantly moving from increasing and falling barometric pressure. There have been attempts to do what you suggest to control hurricanes. In the 1970's, silver iodine crystals were dropped over them to cool the air but it did not work and the project was abandoned.

To control temps, you would have to predict them. Mankind has made a lot of progress in short term prediction of the weather but long term prediction still needs more understanding. Engineering the weather not only seems near impossible at this point, it could also prove to be very dangerous due to unintended consequences.