How can I dehumidify the bathroom while I shower, without using the ceiling fan?
They are feeling cold because the elderly feel drafts like crazy. Turning on the fan conveys hot humid air outside and that air gets replaced with air from the house which feels cool compared to the hot humid bathroom air. 

It also feels cold when water evaporates off your body and if you are removing the humidity from the bathroom moisture evaporation on your body increases thus making you loose heat. 

One option is to install a heating lamp or a new school equivalent. Btw I'm from Toronto ;-p 

Here's a heat lamp exhaust fan
www.amazon.ca 

With this type of unit additional wiring may need to be added.