Depends what you mean by tropical plants - certainly some plants, like Cordyline and some other palms can and do survive here outside. I know there was a banana tree in one part of London 2 years ago which got mature enough to carry fruit outside - but I bet it didn't make it through last winter. Micro climate is critical really.

also you would need to insulate and heat the greenhouse-- i've known the water to freeze in mine and its double glazed

Summer temperatures are plenty warm enough, but for any perennial tropical plants you need to protect against frost as many cannot survive one degree of frost or even low temperatures over a period.
Just to give you an idea, we grow, in a frost-free but unheated conservatory, edible passion fruit, no problems, guava (sometimes the plant dies back from the cold in winter), feijoa (which can resist a touch of frost), Japanese medlar or loquat, and the tops of pineapples (yet to fruit.) We have grown extremely large papaya or paw paws, but they rarely survive the winter due to low temps.
To really succeed with a wide range of tropical plants you would need not only heating, which is very expensive, but also supplementary lighting.
Things like ginger and lemon grass do well though.

I have a few borderline plants like a Zantedeschia sp (giant Calla Lily) and a few amaryllis bulbs but these are bulbs or tubers and they go dormant over winter so storing them is no problem. Some others can be brought in and used has house plants. The other thing you might consider also is that you would only be able to have them outside from very late may until September. So the answer I would say is yes to the more hardy ones and to bulbs and tubers and no to the more delicate ones

I have grown some "exotic" plants, bit they will only last summer as far as I know as when temperatures drop, they may die.

What was the intention of your question, Guest? If you are just looking for a garden which looks tropical there is quite a range of annual and perennial plants you can grow which give that tropical appearance even though they are hardy or easily grown annuals, as suggestions above have explained.

I know that morning glory ipomoea "kiss me quick" look tropical and when the flowers die down, you are left with an evergreen foliage, and then flowrs next year etc...