I have an older home. Last year I didn't have this problem but this winter, to save money I keep my temperature a lot lower. I'm seeing a lot of condensation on the windows and now on my livingroom wall, water running down and mold forming. It also smells like mold in my home. Will purchasing a good dehumidifier help? I am also thinking of adjusting the humidifier on my furnace? Another issue may be that my bathroom doesn't have an exhaust fan but I can't afford to have one put in. I need the best, cheapest solution.
I'd start by adjusting the humidifier on the furnace. It sounds like you don't have to add any additional humidity to the air, so you could probably turn it down (or possibly off).
If you have a gas fired furnace, turning the heat up a bit could help. If the furnace does not have an air intake connected to the outside, the air used for combustion will be drawn in from outside. During the winter, the cold outdoor air has very little moisture. When the cold dry air is drawn into the house, it will lower the humidity levels in the home. This is why loads of people have dry skin in the winter, and the reason humidifiers are installed in the first place.
If none of that helps, you might have to consider installing a dehumidifier, or some other form of HVAC system to remove the excess moisture.
Another issue may be that my bathroom doesn't have an exhaust fan
That's likely the primary issue. Excessive moisture in a short period of time finding it's way to the coldest surfaces. A dehumidifier won't help with that type of moisture issue. Short of a proper exhaust (or just a window) in the bath you are probably better off fixing the issue on the window side of the problem by covering them with the shrink-film. At least the surface to condense on won't be as readily available to the moisture laden air.