Gearing. If its the double crankset, you are in big trouble. You can get a 38 inner ring instead of the 39 stock ring. Not much difference. 25 tooth big cog in back is not big enough. You can get a 10 speed cassette from SRAM and/or Shimano with 11-34 cogs. Low of 39x34 is not low enough to get you up mountains pulling a trailer. Close, but probably not quite low enough. A 39x34 low gear is problematic.
If you have the triple crankset, then you are OK. Replace the 30 tooth inner chainring with a 24 tooth ring. And still get the new 10 speed cassette with 11-32 or 11-34 gearing. 24x32 or 24x34 is a low enough gear to get you up any mountain.
Replacing the cassette will require a new chain. If you have a short cage rear derailleur, you may also want to replace it with a long cage rear derailleur if you change the cassette. Short cage will work, but may be problematic.
Tires. The 23mm standard tires are not wide enough. Get 28mm tires. They will fit your rims and brakes.
Trailer will work fine with your bike. I know someone who pulled a trailer with a Trek carbon racing bike. It was a single wheel BoB trailer but two wheel trailer should pull the same.