If you're looking for low profile all-terrain tires, you may not find the search particularly straightforward. You're unlikely to find a "low profile" all-terrain tires subcategory with online sellers, and manufacturers generally don't produce all-terrain tires that are classified as low profile, specifically.
And so the task of finding a set that is suitably low profile falls to you.
The bad news is that involves some math.
The good news is that it's very simple math.
To determine the side profile (height) of a tire requires an awareness of two numbers from the tire size description -- section width, and sidewall aspect ratio.
As an example let's consider all-terrain tire size 275 60R20.
The two numbers you need to be aware of to determine side profile are 275 and 60. 275 is the tire section width, 60 is the sidewall aspect ratio.
Tire section width is expressed as millimeters. If you're a red-blooded Murican, you might find it more intuitive to immediately convert that number to inches (Google is your friend).
275 mm = 10.83 inches
The sidewall aspect ratio number is expressed as a percentage of section width, so 60 = 60%.
To determine the sidewall height of the tire you'll take 60% (0.60) and multiply it by the section width, 10.83 inches.
The result in this example is 6.5 inches; the sidewall height of a 275 60R20 all-terrain tire is 6.5 inches (from wheel to tire tread).
By comparison, all-terrain tire size 275 55R20 would be a slightly lower profile: 10.83 x 0.55 = 5.96 inches. So about ½ inch less sidewall, i.e. a lower profile than the 275 60R20 tire.
You'll be hard-pressed to find truly low profile all-terrain tires with the look of low profile truck and SUV street tires. Nevertheless, all-terrain tires often have significant and tall sidewalls, and you can use this calculation to at least avoid that…