You should choose your gloves based on 2 criteria: the weather conditions and your skill level.
Horse riding gloves are not just to protect you from the cold. They will also protect your hands from rubbing against the reins, and stop them slipping thanks to their non-slip material. They are therefore important for both your comfort and the quality of your riding sessions.
If you're looking for gloves to protect your hands from cold and bad weather, try warm gloves that are specially designed for winter riding. If you're not in the habit of wearing gloves, go for a thinner model that won't mask the feelings you get through the reins and the aids you give. If you always wear gloves when riding, choose a thick model to protect you from the cold.
Your Skill Level
You can get your horse ready by yourself and do not need help when riding. Choose gloves with a combination of mesh and leather. They provide comfort, contact and durability with a close fit. For optimal grip, choose gloves with non-slip silicone studs.
You can get your horse ready by yourself, even if you still need help with your riding during group or individual lessons. Go for synthetic gloves as they are more durable and help you grip the reins better. Their fitted cut is also very comfortable and the second-skin feel means good contact.
You are starting horse riding and need help with your riding and getting your horse ready. You haven't yet mastered the three gaits. Try knitted gloves with little bumps where the reins are held. Being thin and supple, they won't change the feelings you get because they will fit your hands well. However, they will only give you limited protection from rubbing.