5e leaves much of the adjudication and rule-improvisation to the DM, which means the rulebook does not explicitly say what rule covers each specific scenario that comes up in a game. It falls heavily on the shoulders of the DM to improvise such rules as needed.
There is support for the above statement mentioned in the rulebooks; for instance:
Advantage and Disadvantage
... The DM can also decide that circumstances influence a roll in one direction or the other and grant advantage or impose disadvantage as a result.
(page 173 in the PHB)
It is within your power (and the heavy, heavy responsibility) as DM to rule these things out. For further reading, take a look at The Angry GM’s Marvelous Mechanical Miscellany for Ad Hoc Adjudication and Improvisational Invention. WARNING: SWEARING. Scroll down to the "Modifiers" part, that's what you're looking for, but you might want to read the whole article.
Other things I have, personally, improvised rules for in similar situation:
Concentration Saving Throws for certain situations, as per the Concentration Rules in PHB 203:
The DM might also decide that certain environmental phenomena, such as a wave crashing over you while you're on a storm-tossed ship, require you to succeed on a DC 10 Constitution Saving Throw to maintain concentration on a spell.
There are rules spelled out as you mention, the Chase rules can be found in DMG 252, they are pretty solid and I create my own chase complications table all the time.
The Mounted Combat rules can be found in PHB 198, they're pretty disappointing but I wouldn't modify this too much as the players have access to the same rules.
The Cover rules can be found in PHB 196. Cover grants bonuses to AC and Dex Saving Throws, which make PCs so much harder to hit, entrenched as they are. Tip: throw in some chase complications that flush them out of their cover.
