I know that Equestrian's Gloves in Heroes of Might and Magic III increase my movement points by 300. If I equip two gloves in two ring slots, do I get 300 or 600?
Two pairs of Gloves do not work cumulatively, so equipping Equestrian Gloves twice will increase land movement only by +300.
Artifacts that increase movement (Boots of Speed, Equestrian's Gloves, Necklace of Ocean Guidance, Sea Captain’s Hat) need only be worn at the end of the turn to gain bonus in next turn.
Speed artifacts (such as Cape of Velocity) do not increase adventure map movement, but hero’s creature specialty does. Sir Mullich's specialty does not, however.
Source (I was testing it too myself, but in this .pdf you can find much more than I can possibly write here! Even experienced players can learn new things from it :)
Some other useful informations:
If the hero is moving from one terrain type to another (potential) penalty is calculated based on the terrain from which he is moving into another. So, if you move from grass to swamp there is no penalty, but there is one if moving back to grass.
If a hero attacks a tile beside a wandering stack his movement will deduce based on the terrain from which he is moving into the attacked tile after winning. The same works if a hero is moving onto a map object: he will lose movement based on the tile in which he was standing just prior.
If the hero attacks a wandering stack directly (therefore not moving into the spot the wandering stack occupies) his movement will deduce based on the terrain from which he is attacking. The same works when hero is picking up resources.
In short: only the tile the hero is moving from counts.
However, there is an exception: if the hero moves to or from a road he will not gain any movement bonus. More so, if he steps from a penalty terrain onto the road, or vice versa, penalty will apply.
A hero can visit any movement providing map object as many times as he wants, as long as he fights between revisits.
The distance a hero travels depends on the creature's speed and artifacts at the beginning of the day, not on changes after the day starts. Snow/swamp/sand/rough terrain penalty is calculated for every tile traveled.
All creatures that are 11 or faster are put into a single group with 2000 movement points. So, if you have an unit with 11 speed, while the rest is 16+, there's no need to take it off, as it won't speed you up further.
If your slowest unit have speed 3 or less, then Hero movement allowance is 1500 movement points. The next values for every 1 more speed (from 4 to 11+) (there's a table in the link above) are: 1560, 1630, 1700, 1760, 1830, 1900, 1960, 2000.
Default distance traveled by boat is 15 tiles and is not affected by creature speed.
Each Lighthouse adds +500 to boat travel, but doesn't work until the next day after being flagged. Necklace of Ocean Guidance provides +1000, Sea Captain's Hat +500 movement points. Navigation skill provides +750 per level of skill.
Land and sea enhancing movement artifacts are a separate source, and are added to the Logistics and Navigation bonus, not enlarged by it. Same goes for movement enhancing objects.
Town Portal costs 200 movement points if on Expert level, 300 otherwise.
Dimension Door costs 100 movement points, regardless of Air magic skill.
Sorry for being late with answer, but this is one of these games that "never gets old". I hope it will be still an useful answer!