So I fell down a rabbit hole..
I was able to find a couple of vague references to the game, online. It exists. The main reason you're having trouble finding it is because the series was renamed "Let's Ride" for the North American market. In Europe, it is known by localised translations for "Horse & Pony". The series has had multiple developers since DICE.
I have found a credible source that "Horse & Pony II" was actually titled "Häst & Ponny: Ridskolan (Riding School)"; however, I am personally convinced that the title Refraction Games worked on was actually "Häst & Ponny : Varsågod Och Rid! (Hurry And Ride!)"
According to an archived version of the original Refraction web page,
"Horseback riding in full 3-D, a childrens game, Horse and Pony II was nominated for best Multimedia Title in 1998 at the Europrix Awards (http://www.europrix.org/). The game was produced by o2 interactive Media. Refraction contributed a 3d section, placing the player competing in three different games. The title is a bestseller in scandinavia and is just about to be realesed [sic] in England and other european countries."
- "Product Spotlight" @ refraction.se, captured Feb 26, 2000
I also found an interim report, published by DICE in mid 2000. In this report, they list "Horse and Pony IITM" as a game launched in 1998 for the PC. It is also listed as having sold 200, 000 copies. Earlier in the document, they talk about a game that is (at the time) being developed; "Legacy of Rosemond Hill". In particular, they say "The game will be launched as a PC version in the autumn in Europe by Pan Interactive". This is important.
At this point, I can't find any more references to "Horse and Pony II". But hang on, evidence suggests that this was a popular game in Sweden. I'm not overly familiar with video gaming in Sweden, but wouldn't they call it "Häst & Ponny"? That's the Swedish translation of "Horse and Pony".
After very little digging, I found a portfolio page for the lead game art producer for both "Horse and Pony 1 & 2". They further confirm that the games were developed under Pan Vision, who were Pan Interactive before 2001 source. This is where things get a little complicated - the box art does not say 'Horse and Pony 1' or 'Horse and Pony 2'. Instead, the box art reads "Häst & Ponny: Min Första Ponny" and "Häst & Ponny: Ridskolan", which translate to "Horse and Pony: My First Pony" and "Horse and Pony: Riding School", respectively. Due to the clear graphical improvements, "Horse and Pony: Riding School" is the newer title, and would be "Horse & Pony 2".
After following a link provided on the above mentioned page, I found a channel on YouTube that shows off "Horse and Pony: Riding School". However, I also found a video for a game titled "Häst & Ponny : Varsågod Och Rid!", or "Horse and Pony: Hurry and Ride!". This is where things get a little more complicated. The description in the video suggests that this could be the game you are looking for:
"Horse & Pony : Hurry and Ride, also know as Let's Ride (released in 1999 in North America) or known as Häst & Ponny : Varsågod och rid! (Sweden) is a horse game released in 1998"
"- Horse & Pony : Hurry and Ride! / Häst & Ponny : Varsågod och rid! / Let's Ride! (Horse Game)" video description @ youtube.com
This game was released in 1998, and brought to the North American market in 1999. This supports the original information I found on Refraction Game's original website. Furthermore, looking at the three videos, it mostly uses 2D or static 3D graphics. In fact, the only non-static 3D graphic appears to be the player character, when performing in competitions. This appears to be the component Refraction Games contributed to the title.
According to the description in the above mentioned YouTube video, the "Horse and Pony" franchise was also known as "Let's Ride!". This lead me to the "Let's Ride' page on Moby Games. While the early games do not appear to be listed, we do see a listing for "Let's Ride! The Rosemond Hill Collection". Following the link, it confirms to include "The Legacy of Rosemond Hill", the other horse riding game that was directly attributed to Refraction.
Eventually, this lead me to a page on the "Pferd & Pony series". Pferd is horse, in German. This page lists over twenty titles, across PC and Nintendo platforms. The last entry is dated 2017, and is a 3 in 1 compilation of three previous titles. It is clear that neither Refraction Games nor DICE had any input in any of the other games, including the two additional games that make up "Let's Ride! The Rosemond Hill Collection". The only thing that is common between the three titles is that Pan Interactive published them - however, they are also credited for conception of the series.
If you would allow me to speculate further, I interpret that Pan Interactive / Pan Vision outsourced the development of "The Legacy of Rosemond Hill" to DICE, after Refraction Games contributed to their earlier title. They continued to produce more titles in the series, which has come to be known under the series name of 'Horse & Pony' in Europe, and "Let's Ride!" in English-speaking countries.
It appears that we have a more credible source referencing "Horse & Pony 2" as the "Riding School" title, but I am more convinced that it was actually the "Hurry and Ride!" title that Refraction Games worked on.