Missions related to the main story are indicated on your map with a yellow circle and the initials of the person involved. The image below is the map icon of a story mission given by Javier Escuella:
Stranger missions are optional side quests given by NPC's around the map, they usually show up when you are in close proximity to them and are similar to story icons but white. The will often have a '?' symbol or once you have started the first quest in the series they will have the 'strangers' initials.
Pelts and animals can be sold at the butcher for cash, at the Trapper for cash and to craft special outfits or donated to Pearson at the camp for satchel and cosmetic camp upgrades.
Ammo can be bought from Gunsmiths and General Stores, bullets can also be found around camps and defeated enemies.
All the icons tell you what they represent when you move the cursor over them.
As for your horse, you should have a temporary one given to you as part of the story and pressing up on the D-pad will summon your horse to your location, if it's close enough. Otherwise it is shown on the map with a horse's head icon.
If your horse has died then you will need to either buy another from the stables, steal one, or progress the story until you are given another one.