Notes:

These class features were created to replace the Natural Explorer ability and it's improvements for the Ranger in the D&D 5e Player Handbook. The goal was to give the Ranger abilities that can be used in most campaigns while still having the flavor that is specific to the player character's favored terrain. Due to the changes made with Greater Natural Explorer, it is probably best to replace the level 8 ability Land's Stride with Fleet of Foot from the Revised Ranger Unearthed Arcana (reprinted here) to avoid any redundancy regarding traversing difficult terrain.

Natural Explorer

You are a master of navigating the natural world. Beginning at 1st level, you gain the following benefits when traveling for an hour or more:

Difficult terrain doesn't slow your group's travel.

Even when you are engaged in another activity while traveling (such as foraging, navigating, or tracking), you remain alert to danger.

If you are traveling alone, you can move stealthily at a normal pace.

When you forage, you find twice as much food as you normally would.

In addition, you have gained exceptional skill at navigating your favored terrain.

Terrain Ability Arctic Your body has become more durable against the harsh environment around you. You now have resistance to cold damage and can ignore the effects of extreme cold. Coast Your time around the water has trained you to navigate it nearly as well as you can dry land. Your swim speed is now 30 feet. Desert Your mind is trained to see through the illusions and tricks the desert heat can play on the mind. You gain proficiency on Intelligence (Investigation) checks and can ignore the effects of extreme heat. Forest Trees provide an excellent means of cover and can give you an ariel view. Your climbing speed is now 30 feet and you have advantage on Wisdom (Animal Handling) checks with woodland creatures. Grassland You have learned to move quickly in order to keep up with your prey. Your movement speed is increased by 10 feet. Mountain You've become as strong as the earth around you. You have advantage on saving throws against being shoved or knocked prone. Swamp The hidden powers of the mires have taught you a few lessons. You learn the Poison Spray cantrip. Underdark Those who cannot see here become nothing but prey to those who do. You gain darkvision to 60 feet, or if you already had it, it is now extended by 30 feet.

Greater Natural Explorer

You have honed your ability to maneuver the natural world even further. Beginning at 6th level, you gain the following benefits when traveling for more than an hour:

Your group can't become lost except by magical means

While tracking other creatures, you also learn their exact number, their sizes, and how long ago they passed through the area

You can move through difficult terrain without spending any additional movement

Additionally, You have gained an additional benefit related to your favored terrain, listed in the table below.

Terrain Ability Arctic Whenever you roll initiative, you gain temporary hit points equal to half your ranger level (rounded up) plus your wisdom modifier Coast You can now hold your breath for three times as long, and your swim speed increases by 10 feet Desert You now gain expertise in Intelligence (Investigation) checks Forest When attacking from an elevated position you gain a +2 bonus to damage rolls Grassland You now have advantage on iniative rolls Mountain You have advantage on Strength (Athletics) or Dexterity (Acrobatics) checks when making or defending yourself from a grapple attack Swamp You gain resistance to poison damage and have advantage on saving throws against poison Underdark Your darkvison now allows you to see through magical darkness

Beginning at 8th level, you can use the Dash action as a bonus action on your turn.

Adaptable

Your experience navigating the wilds has led you to become adept in another environment. Beginning at level 10, you gain the abilities of a second terrain in addition to the ones you already have.