To get the Hyrule Bass head to the lake by the Temple of Time. Swim to the middle small island and watch for fish swimming in the water. When you see one launch a Remote Bomb into the water and detonate it. If you got the fish it will float to the surface. Just swim over to it and get it.
The Wild Boars are in the Forest of Spirits. Enemies will also attack the boars so watch out for that. They are pretty fast and pretty easily spooked so you might have to give chase. Arrows are probably the best bet to take one done but you can also get lucky and one will charge you for a easy kill.
Head back to the Old Man’s Hut and go into your Materials tab of the Inventory. Select Spicy Pepper and hit the X key to hold it. Then A to add it. Now hit A to add for the other two items (Raw Meat and Hyrule Bass). Standing in front of the Cooking Fire outside the Hut with all three items in your hands hit A to cook. You will make a Spicy Meat and Seafood Fry. Restore 5 hearts and 3:30 of Cold Resistance.
During the night, before bed, the Old Man will be sitting by the Cooking Fire. Talk to him then and select “I Cooked Something” and he’ll give you the Warm Doublet. If he is not by the Cooking Fire you can sit at the Fire and select wait until Night. When you come back he will be sitting by the fire.
You can also acquire the Warm Doublet by climbing to the top of the coldest peak in the starting plateau area. I climbed it for fun on my way to the cold shrine area, and the Old Man was standing up there. He complimented me on making it so far without warm clothes, and he gave me the Warm Doublet.
After leaving the Plateau and coming back, it is reported by others that the Warm Doublet exists in a new chest inside the Old Man’s cabin if you haven’t already gotten it. Someone else even has said they bought it somewhere for about 80 rupees, but this is unconfirmed.