Choosing air-conditioner's BTU power for humidity
"Dehumidifying cool areas" is a serious trick

It's a common problem in England too, where it's called "the damp". 

The crux of the problem is warmer air can hold more water than cool air.  100% humidity at 10C may be 30% humidity at 25C.  That's how air conditioners and dehumidifiers cool the air.  If they chill air to 10C, it can't hold much water, so water condenses until it is 100% at 10C.  Then it warms back up to 25C and is only 30% humidity.  

However the refrigerant method breaks down at low temperatures, because it's hard to get much cooler than 10C without the evaporator coils freezing.  

You have two ways to go from here. You can then heat the air (which dries it out), or you can use a dehumidifier that is efficient at 10C.  The best bet for that is a desiccant dehumidifier.  It uses desiccant (similar to the little pouches found in medicine bottles and consumer products) arranged in a disc. Air blows through most of the disc, allowing the desiccant to attract moisture from the air. In a small wedge of the disc, hot air blows through to dry out the desiccant for the next pass.  This hot, humid air must be ejected outside, it cannot collect water in a bucket. 

If you want bucket collection, you are stuck running a refrigerant dehumidifier inefficiently. 

Heat alone is enough

The simplest way of dealing with cold-temperature humidity is to warm up the air.  The warmer air holds more moisture, which lowers the relative (%) humidity level. 

Using an air conditioner as a dehumidifier

Since they work on the same principle, an air conditioner won't be any more effective than a refrigerant dehumidifier.  It simply disposes of the hot air externally, causing net cooling. 

A BTU is the energy needed to raise 1 pound of water 1 degree F.  A pound of water equates to a pint equates to a half litre. 

Water's latent heat of vaporization is well known as 970 BTU (per pound,  obviously).  You need to move that much heat to vaporize or condense water.  Now, in the HVAC business,  when they say "BTU" they actually mean BTU per hour.  But that gives us a rough idea of the dehumidification power of an air conditioner: a 9700 BTU air conditioner will wring out 10 pounds/hour, or somewhat less than that due to inefficiency.