I have an inside workshop with a few smaller machines (2.5" lathe, sensitive drill & hand shaper) and it is very convenient in the winter.
The flooring is covered with carpet tiles (which can be moved and replaced as required) and I don't wear any special shoes or clothing – just an apron when working. The lathe stand has side & back screens and a movable Perspex front screen – most useful when milling. I only work with non-ferrous and mild steel inside (not cast iron) and never use the grinder or T&C cutter indoors either (I do hone though – which is usually quite sufficient to keep my tooling sharp). I vacuum fairly regularly. It works well and there have been no complaints from my Manager (in fact I get completely banned from the main workshop on very cold days – something to do with previous bouts of nasty colds and coughs keeping her awake).
My main workshop (an unheated garage) is used only occasionally at this time of year – and only for any 'dirty' work (all cast iron, power shaping & sawing, heavy milling & grinding). It's unheated but in short bursts quite usable – so I try to plan my work to measure & mark-up inside and do any outside job quickly – again leaving anything that can be done inside for later. With a little thought this seems to work very well.
Taking a longer view of the year also helps – smaller items can be done in the winter and larger work (or material preparation) – that needs the bigger machinery, planned for the warmer months when possible.
As with any advice on here – this approach clearly depends on the type and size of work you are planning to undertake – and whether you have the luxury of some duplicate machines and two workshops. However a small lathe and drilling machine can compliment larger machinery quite well and they don't need to be very expensive (at least mine were not).
Regards,
IanT