Do dry wheel bearings increase drag? My kid trailer I have had for a few years has, in the past few weeks, been noticeably harder to pull.  I checked it over and I found that not only are my wheel cones are a little loose, that I can spin the axle with very little resistance.  When I say little meaning I can give the quick release lever a light flick and it will spin 4 or 5 times easily with the wheel in the vertical orientation (off the trailer).  I'm assuming that this is because the bearings are dry, and since anything I have rebuilt myself, the grease (park tools polylub 1000) will give some drag to keep it from free spinning.

I have pulled it for hundreds (if not thousands) of miles to this point without really any problem.  This summer it has been in the rain twice (~4 miles), but I noticed this new drag before.

Trailer (shaped object) is a Pacific Voyager II sold through Toys-r-us (best that I can tell).  I don't know the service history (assuming none) and I'm the 3rd owner.  When I got it I replaced the tires on it (20" Kenda road tires) and keep the pressure high (50lbs of 55lbs max).  At around the same time I also upgraded the hitch system to a standard Burley one so I no longer have the spring in the system causing tugging.
If your wheel can spin freely around the axle, there's two scenarios here:


You've got super awesome bearings that have held up really well and still rotate freely.
The bearings are actually really tight and not moving at all and the wheel rotates on the axle itself.


Either way, since you mention the cones are loose, you should pull apart the hub and check the bearings. Look for dirty grease and see how the bearings/races look. Clean and repack if necessary.

New grease will always add a bit of friction, but as it breaks down and heats up (during use) it usually becomes more viscous, therefore reducing friction.