No, a US garden hose is not easily connected metric threading (on the brass tap) and no threading on the plastic tap.  In Europe these smaller rainbarrels are used primarily to fill watering cans rather than connecting a hose.  The water in a rain barrel flows only by gravity – it will not be a pressured flow like water from the tap on your house.  If you want a hose, we recommend looking for rubber tubing at a home supply store and using a hose clamp to fix it in place.  A tube can be attached to the nozzle of the plastic tap and the brass tap has a separate nipple that can be attached if you would like to attach a tube.  Depending on the diameter of your existing hose, you may be able to cut off the threads and attach your hose by using a hose clamp.