Plants from temperate regions like Europe, slowly harden-off as a gradually cooling winter sets in, whereas plants, which come from sea, or near to sea level in the tropics enjoy year-round heat, and will almost certainly not survive a winter in the UK. When subjected to temperatures below 16°C these plants shutdown, and growth will usually return when the temperature rises again if the duration of cold was very short-term. Temperatures in the single figures usually means death to these plants, I have witnessed mature Coconut palms that have been totally defoliated by 4 hours of -3°C and have survived, however, this is a rare exception and Coconut seedlings will usually die after one week of temperatures below 14°C. Plants from mountainous regions of the tropics can, to some extent tolerate freezing temperatures, however, the temperature extremes occur between the day and the night times not so much summer and winter. These plants can die when exposed to extended lengths of cold temperatures in the British Isles.
The tropical plants that we can grow to some extent in the warm temperate climate of the British Isles are those that periodically suffer physical stress in their home environment. The best example comes from those plants that come from regions that have a distinct seasonal dry period. If it already has the cellular structure to handle the physical stress associated with dryness (specialised stomates, extra layers of wax to reduce transpiration, more rigid cell walls resistant to collapse under conditions of low water pressure), then it can presumably handle cold. Cold produces many of the same stresses that are brought on by a prolonged drought. During a cold spell, a plant's ability to absorb or translocate water is severely reduced as its own cells function less efficiently at the lower temperatures. In addition, water in the form of ice crystals is no longer available for absorption or translocation. Thus cold causes a physiological drought.
Therefore, tropical or subtropical plants that are adapted to survive the stress of low water conditions (no matter what underlying conditions are causing it) will have a better chance of weathering a cold spell. Plants that grow in semi-arid areas, savannas, exposed sandy coastal areas, and on exposed well-drained rock faces are prime candidates for testing in colder climates.
A sudden freeze is far less devastating than an extended cold spell on tropical plants, planted in an area where temperatures seldom drop below freezing. The length of time and depth of a hard freeze, wind speed, and ambient humidity can also influence how destructive a cold spell might be.
Desert plants in particular usually suffer extremes of heat and cold. Temperatures in many desert areas can plummet to -25°C, which is far colder than anything we are use to in the British Isles. Yet plants that endure these hostile environments quite often die at -3°C or -4°C in the British Isles. The reason for this is our prolonged wet winters with ambient humidity and cold waterlogged heavy soils.
A sandy soil is much preferred over a clay soil for growing tropicals. After cold spells clay soils are very slow to warm up. Experience shows that tropical plants can survive short cold spells if planted in a sandy soil, where as, the same plants would certainly die when exposed to the same temperatures if planted in a clay soil.
A plant sheltered by other trees and shrubs is more likely to survive than one planted in an exposed site. Other contributing factors as to how successful a plant will be handling cold is determined by the plant itself; its age and size, woody plants are much more cold hardy when older, and palms in particular ought to be raised under glass until pot bound in at least a 5 litre pot before being planting outside. The overall health of the plant specimen itself at the time of the cold spell can make a huge difference. A healthy, happy plant will be much stronger and able to withstand cold better.
To make healthy (happy) plants you should; plant in a deep sandy, well draining soil. Apply a 20 to 25 cm mulch of partly decomposed garden compost or leaf-mould to protect from frost and retain surface moisture. This should also be done during the summer months to avoid dehydration. Avoid heavy pruning in late autumn. This encourages tender new growth that can be damaged by an early frost. If it is an evergreen or especially a palm, apply a fertiliser that has a high potassium and low nitrogen content in the early autumn at least 45 days in advance of an expected freeze. This strengthens existing foliage. And try some of the many ways growers have developed to minimise the damage caused by freezing.