The kingdom of Arnheim is a vast region. Around Rikhaven Bay, the temperature tends to be warmer. Further north and in the mountains, it is much colder. Just ballparking, but from north to south, the kingdom of Arnheim is 850 miles. Consider the difference in temperature from Rome, Italy to Copenhagen, Denmark (about 830 miles).
If I look at the continent map, though, I can see that mountains dominate the kingdom of Arnheim. Those mountains are very cold. I would definitely consider the dominant terrain of the kingdom of Arnheim to be cold mountains.
Cold mountains mean Dwarves.
I’m using the steps outlined in Kent David Kelly’s excellent Game World Generator Deluxe Edition, which you can pick up here. With 434 pages of world building goodness, it is an absolute steal at $3.99 and even goes on sale below that.