The problem with some of those plants won't necessarily be just the cold but the sunshine hour/heat needed to produce viable fruit. If you look at pfaf.org it will give you a good idea of what is more/less viable bearing in mind the cultivation details are written from a southern England perpective. Thats not say it can't be done with microclimates but that it might be alot of work. Maybe it is less cloudy up in southern Finland?!
http://www.pfaf.org/user/plant.aspx?LatinName=Diospyros+virginiana
"The fruit may not ripen properly in a cool summer, though if it is frosted it normally develops a very good flavour[K]. The fruit can also be harvested in the autumn, preferably after a frost, and bletted. (This is a process where the fruit is kept in a cool place and only eaten when it is very soft and almost at the point of going rotten). Much of the fruit on trees in a relatively sunny position at Kew after a relatively warm summer in 1996 was still not fully ripe, though it was very nearly so and ripened well off the tree[K].'Dooley' grows well near the northern limits of persimmon culture."
-So you might be alright if you blet it. I couldn't find a source of the named cultivars in the U.K unfortunately.
http://www.pfaf.org/user/Plant.aspx?LatinName=Asimina+triloba
"The mature fruit is rarely seen in Britain[182], only ripening after a long hot summer[200]. A small tree growing against a south-facing wall at Bristol Botanical Gardens had a small crop of immature fruit in early September 1996 (following the hot summer of 1995) - this was the first time it had been seen to bear fruit[K]. Flowers are formed in the leaf axils of wood produced the previous summer"
-So you you need two successive hot summers to get any fruit!-This put me off growing it which is a shame as custard apples are my favourite fruit.
There are some Juglan varieties like hickories and walnuts more suitable for growing in Britain, can't remember the names off the top of my head though so I will see if I can find them for you.
You might be able to grow a hardy variety of fig in a favourable spot if you can keep the temperature above -15 C e.g brown turkey or hardy chicago.