It can be darn cold in the mountain parks of North America even during the warmest months of the year - the problem is the high elevation of many of the mountain parks, and the katabatic winds (downslope winds) that are common in mountain areas.
If you are thinking of buying a sleeping bag in North America, be aware that there are two broad categories in the marketplace: 1) What parents buy their 12 year old so he/she can sleep in a tent in your back yard during July - this is about 90% of what is on the market, and; 2) High Quality stuff that is sold to folks who are interested in serious camping or hiking. Obviously you will be interested in the second category only, which you will find at specialty shops and not in the 'big box' retailers. Plan on spending perhaps $300 or so for a good sleeping bag, bag liner, stuff like that.
It would also be to your great advantage to try and purchase the sleeping bag from a specialty retailer who is close to the mountain parks, and is thus familiar with what is needed for mountain camping. If you go shopping in the UK or in New York City, you will likely find that the sales staff are not aware of what is needed for mountain camping, and that the shop likely doesn't stock the best selection of what you are looking for.