A dehumidifier works (I am assuming) by drawing air at the ambient temperature over a cooling area where the air temperature drops past the dew point and water condenses out.
The higher the ambient temperature the more moisture the air can contain and so running increasingly warmer air over a roughly 0C matrix will extract more moisture.
Alternatively the dehumidifier may be able to maintain say a 10C temperature drop over ambient and so perform much the same from about 10C upwards.
The issue this time of year is with outbuildings where the ambient temperature is just a few degrees C )if you are lucky).
As most of the moisture has already condensed out, potentially there is little more a dehumidifier can do.
O.K. - so warm the air up first and then dehumidify? Although once warmed the air will probably have taken up the water and then there is no more humidity problem.
Alternatively, warm the air up and then pump it outside (with the humidity condensing at the outlet in a nice cloud of vapour) and replace it with external air at about 4C which will have relatively little moisture.
This could be an extractor fan at one end and a fan heater and inlet vent at the other.
Given that as far as I can see you have to warm the air up anyway before the dehumidifier can work, would this venting warm moist air and replacing with cold dry air be a cost effective method for the winter? Given also that dehumidifiers seem to cost around the £200 mark for good ones.
This also applies to camper vans and caravans (cars too, I suppose). In the winter they are prone to condensation because of the inability of the air to hold much moisture, so condensation settles out everywhere unless the interior is warmed up. So, again, dehumidifier or just bung in a fan heater and open a roof vent so the air warms up, picks up moisture, rises and takes the moisture outside? Downside is that you end up with a warm room containing moisture which will just condense out again unless you are very sure that you have replaced all the moist air with dry cold air before turning off the heating.
Cheers
Daver