I am an opportunistic portraitist and usually conform my choice of gear to the other variables in question. Like you, I live in a place with long winters, so an indoor lighting set-up is a must unless I want to confine my portraiture to subjects standing indoors next to windows or outdoors dressed in ski gear.
Other practical considerations revolve around how much light you need. The advantage to an indoor strobe set-up has always been that standing under 1000W of hot lights is, well, hot. If you are using an LF camera and your widest aperture is f:5.6 or f:8, you are going to need a lot of light and strobes are often the easiest way to get it. This is particularly true once you start to diffuse the light at the source. If you wish away these practical considerations, then there is no difference - photons are photons. But practicality gets most of us in the end.
I started another thread on APUG about LED lighting, as it seems like that technology might be ready for prime time without the heat caused by incandescent lights. But it doesn't seem like anyone here at APUG is using LEDs yet, and so no useful comments have been offered so far.
So for now, it is mono-lights and softboxes during the winter.
In the summer, I have painted two 4x8-foot plywood pieces white and screwed them into the east side of my barn. Makes a nice impromptu portrait studio on summer afternoons. I would rather shoot there than indoors -- it is just more pleasant.