Look on my profile and you will see a photo of a dapple grey Irish draught/Connemara mare - my DiDi. She is registered with the Irish Draught Society.
Irish Draughts themselves are a stockily built ride and drive tall horses with a broad back, big butt and deep chest. They make excellent fox hunters. They have been used in the past to beef up other breeds of horse who lack substance. However IDs are not cart horses neither do they have much feather.
It is common these days to cross them with Connemara ponies who have a height limit of 14h2 max - so if you blend the two breeds you get something like my DiDi who is 15h2. DiDi's mum was recorded as "Molly" probably a Connemara
Irish sports horses, a relatively new "breed", usually have some throroughbred in the genes as well as Irish draught but they are bred to be lighter in conformation.
Most Irish horses, except perhaps for the racing TBs, are good doers - the Irish climate being ideal for growing nutritious grass. But if the horse was born on the west coast they will be hardy because of the proximity to the Atlantic Ocean with the wind and the rain.
Temperament is invariably"kind". But they can also be highly intelligent. They are strong with lots of stamina.
But as with many breeds, it is their upbringing that decides temperament as much as the genes.
In the UK they are not that easy to find for sale - you can find them but you won't have much choice. Price is usually higher than average. Look on the web for Irish Draught Horse Society site - there is one British and one Irish site.
DiDi's temperament is exceptional - you can get right in close to this girl without fear or hesitation. She'll not hurt you. My DiDi is a good looking, powerful, fast, intelligent, forward going, sensitive mare who can twist me round her front feet. She is up to any weight of rider, despite her relatively small size by European standards. However she is a touch skittish and she needs to feel confident in her rider - she is not a novice ride.
She has a broad back, a big butt and a deep chest but she'll go, when asked, "on the bit" and is never on the forehand. You merely have to think it and she knows instantly what you were thinking. She is a crafty Irish huzzy - and that in a way is a compliment.
If you know what you are doing with horses then buy one - providing you get the impression that the horse likes you as much as you like the look of it.
Traditionally one of Ireland's biggest exports have been horses. They do well at both flat and jump racing. Look up on the internet "The Grand National" and you'll find a long list of Irish bred winners of what arguably the world's most arduous race.
What more can I write?
PS If you search for "DiDi" , then you'll find her name mentioned in posts I have written.