Nowadays in Britain, English style riders are taught from the very beginning to ride
collected and to be moving towards riding 'on the bit' - regardless of whether they are thinking of moving into dressage.
Most of the older riders who decide to take lessons from most modern instructors
are also taught to take up contact and move towards riding the horse 'on the bit'
- providing the horse will accept and respond to being asked to 'go on the bit' and providing the rider can adjust his/her seat accordingly.
Any horse being ridden in this way can be given its head instantly by allowing the horse more rein and thereby more freedom of the neck. So when conditions permit the horse can be ridden on the buckle - ie a loose rein. Partly this is done to give the horse a break. But should conditions change then the rider will instantly take up contact.
Once one has come to ride 'collected' or 'on the bite' then riding 'long and low' on a loose rein perhaps held in one hand feels 'strange'.
A modern English schooled rider, visiting the US, being asked to ride a Western horse might well feel nervous out on the trail, in unknown countryside, on an unfamiliar horse, in a very different saddle. Such a rider would be tempted to take up close contact with the horse's mouth and with levered bits that would be inappropriate. Such riders, even those having their own horses back at home, should be shown how to adopt the Western style.
If one visits a trekking centre in Wales, one invariably is asked to rides 'long and low' but otherwise in English style because the horse has been trained to accept riders of all competence levels. These horses are not used to being ridden 'collected' because many of the customers do not have a firm seat. These trekking horses are ridden in line and they are amazingly controlled largely by the voice of the leading rider - the trail leader (who very often is riding his/her own or regular horse which may well be trained to be ridden collected).
In the semi rural environment of outer suburban towns where vehicular traffic is a constant hazard, it is wiser and safer to keep the horse on a short rein at all times.
The theory being the rider contains the horse at all times and only lets it go when conditions are right.
It is noticeable to me that many American riders learn and practice riding bareback. It is rare to see a rider riding bareback in the UK other than when perhaps one goes out to collect the horse from the field. No trainee is ever sat bareback even in the arena under tuition - the insurance companies would not like it.