And so, this post gives details and images for 4 mountain types, for the purpose of determining the amount of time, or number of slope lines, that a mountain represents for the prospective climber. There are many more than 4 types of mountain in the world ~ but this number should be sufficient for a DM's needs.
In its most extreme form called a glacial horn, this describes an angular, sharply pointed mountain that results from cirque erosion, due to multiple glaciers diverging from a central point. See also Nunatak.
The example on the left is the famous Matterhorn, found on the border between Switzerland and Italy. The modern climb usually consists of 12 to 15 hours, with the benefit of a cable car that enables the first 963 meters to be skipped over. The full climb, including the cable car section, from the base of the mountain to its top, is 2,858 meters (that's counting from Zermatt in Switzerland to the peak.
The time necessary to climb a mountain like the Matterhorn would likely be excessively greater than the modern period, as most of the equipment we now take for granted wouldn't exist. In point of fact, it might even be impossible to fully climb a mountain like this with 17th century equipment.
This is a narrow ridge of rock that separates two valleys, which is typically formed by two glaciers eroding parallel U-shaped valleys.
The example on the right is the Striding Edge in England, near Ullswater. The modern climb usually requires about 5 and a half hours, from a point only 48 meters above sea level. The total ascent is 908 meters.
As a mountain like this is usually done with minimal climbing gear, the difference between a modern day ascent and the time of my game's world would likely be very little ~ though it must be noted that much of the actual trail on a mountain like this has been tailored and worn down by untold thousands of day visitors.
Fold and Thrust Belt
Yamnuska is the first "mountain" that can be seen along the highway that goes west into the Rockies. It is just a tiny little thing, mostly notable for being stuck out by itself and looking like a ridge-back dinosaur, complete with head, when viewed from the highway. The larger, higher mountains further to the west are of a similar geology, only higher and snow-covered.
I will skip a picture for this. Conical hills may be of any size, as large as Mount Fuji in Japan or ~ like a shield volcano ~ as vast as Mount Kilimanjaro. The time necessary to climb such a mountain, the number of "slope lines," as it were, is more a matter of total distance of the slope, affected by the degree of incline, the presence of snow and the total altitude (as a very high altitude, above 10,000 feet, tends to slow climbers due to a lack of breath, so that slope lies become shorter and shorter as one nears the summit.
Well, that might be a bit to simplistic to build rules upon, but for the present I'd rather not get too ambitious. Hopefully, the rabbit hole that mountain climbing is proving to be won't make it too difficult to complete.