The peak of the horse population in the United States was 26,493,000 (both horses and mules) in 1915. In 2006, the United States had around 9,500,000 horses, and the United States Census of Agriculture for 2007 (table 31) counted 283,806 mules and burros. Between 1915 and 2006/7 the horse and mule population declined 63.07% in the United States.
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In Sweden, the decline of the horse was less due to the rise of the car and more due to the rise of the tractor - horses were mostly kept for labour on farms and not for travelling.
1920 there were about 700 000 horses in Sweden. In 2004, there were 283 100. Harness riding being a popular sport has probably led to a high number of horses remaining. Due to the rising popularity of riding as a sport, as well as some agriculture and services trying out horses as a cheaper and more enviromentally friendly way to handle some tasks (like timber pulling, grass cutting and harrowing) the number has risen to 362 700 by 2014.
So, it has decreased to 51,81% of peak numbers by 2014, but was down to 40,44% in 2004.
Declines in horse population and usage weren't so much because of the car, but because of the tractor (for farming) and the motor truck (for local delivery). In addition, the electric streetcar supplanted horsecars on street railways.
Interestingly despite the glory of racing teams such as Auto Union and Mercedes Germany before WW2 didn't see a rise in the use of the car anything like the UK, USA or France.
Germany began WWII as a nation that didn't have a high car ownership and subsequently relatively few auto mechanics, fuel stations or auto factories. The military relied very heavily on the horse for transport even in WW2 though this wasn't seen to much in newsreels as the rather few mechanised units were given prominence. Movies about WW2 rarely show the low level of mechanisation in German forces.
Source: The War in the West - James Holland
