I can explain my method, hope that helps. =)
Before doing anything to the pony, I would wash the pony, so you have a clean base and a better view of its actual color. Also, your added paint won't be sticking to grime or stuff like that.
Then I would firstly re-pink the hair and then sculpt the horn at the end and then touch up the symbol. I've never done re-pinking before, but I've linked some reference bellow and I'm sure you can find more about it on the internet.
For the material to choose, my premium choice would be Apoxie Scult or any self-hardening polymer clay like Green Stuff or Sugru, but it's expensive and difficult to find. It's sturdy and holds on the vinyl quite well.
Another material is air-dry clay, you can find it in craftstores and it's cheaper and lighter. Though, it doesn't stick to the pony very well so you'd need to glue your piece on it or else it will just pop off. It is also more fragile and if the piece is long and thin (like a horn), it would probably snap if the pony were to fall off. I use air-dry clay to patch up some very small gaps such as bite marks. (I have repaired a chewed horn with air-dry clay) You also have to keep in mind that the clay will reactivate with water so you will have to varnish the piece before getting on to the paint job to prevent the contact with water and risking some issues.
The last thing I can think of but that I do not use is a polymer clay that needs to go to the oven, such as Sculpey or Primo / Fimo clay. It is easy to work with and it is sturdy, but you'd have to cook the piece separetely. That makes it an issue because you can't scult on the pony and make it seamless. You would have to find some serious workaround to make your pony look as if it didn't get any repairs.
As for the sculpting itself, depending on the size of the piece, I would probably use wire and/or aluminium foil for the inside so it saves up some material and keeps the piece lightweight (Especially for polymer clays). It would help to keep the horn straight if youre inserting a wire in the middle of the horn base, glue that wire and then sculpt over it with your material of choice.
If you want to make your pony look like it had never had her horn chopped off, you'll have to keep some reference picture or a reference Powder Pose pony by your side so you don't deviate from your goal.
There are a lot of tutorials on Youtube on how to use your material properly.(See references bellow) You can also try it on something else before working on your Coco Berry so you get the hang of it. The other tips I can think of are : If your self-hardening polymer clay is too sticky, wait a few minutes for it to cure a bit until is becomes more workable for you, but don't wait too long as it will not me workable within a few fours. When you've sculpted a rough shape of the horn, letting it cure a few more minutes can help you add in the details. Use water to smooth out any bump and integrate the clay to the vinyl as best as you can so after the paint job, your pony will look as new.
When you're done sculpting, leave your piece harden 24h just to make sure it is rock solid. At that point, use very fine sandpaper to make sure there are no more traces, fingerprints and make the piece fit in extra flush on your pony.
For the paint job, I would suggest using Gesso as a base coat first, it will help you have a white base to work with (so you can choose your color better and you'll need less coats of it to make it look opaque) and it helps the paint addhere better to the material.
You can use an airbrush, which makes a great coverage because you won't get brushstrokes, but it is hard to work with and maybe you don't have one. You can also use regular brushes which are cheaper. To prevent brushstrokes as much as possible, you need to water down your acrylics and apply very thin coats, one at at time and wait for the previous one to fully dry. That will take a while, but the result will be worth it. This applies to your paint and the gesso as well.
Then, it's a matter of mixing the best color to match your pony. Acrylic paint is my first choice, but be aware that when dried, it will look darker as the wet version of your paint so keep that in mind when trying to match the color to the pony. Do NOT use nail polish. For some reason, that's a thing among some customizers but I will never recommend it.
To finish it off and protect the horn, I would use a matte varnish for acrylic paint, something like 2 coats should do. Use that in a well ventilated area and wait for the first coat to dry fully.
Now that I have explained what to actually do, you also have to have a proper mindset in order to get the best result you want.
That restoration project will take a lot of time, patience and effort. Always stay delicate, never be in a hurry. You can pause your project for a few months if you need to, but do not, in any way, try to rush it.
Here's some reference to help.
http://www.mlppreservationproject.com/body.htmlhttp://www.mlppreservationproject.com/hair.html#RePinkingYou can also see how customizers proceed to make body modifications by looking at their youtube channel. Dollightful is (to me) an amazing customizer and she explains things very well. She makes customized dolls, but it gives a great insight on how you can translate that to pony restoration.
On this project, she used mainly air-dry clay. At the 15:20 mark, you can see the pieces popping off and how she fixed the issue.
https://www.youtube.com/watch?v=DeOCoWs2qhsOn that project, the used mainly apoxie scult so you can see how that behaves.
https://www.youtube.com/watch?v=0RnTdqjZHPcAs for touching up the symbol, I would pick a matching acrylic color as mentioned before, using a very fine paintbrush and only painting the missing areas. If the rest of the symbol is intact, leave it as is. It will help you get your colors to match and respect the shape as well. Always keep a close eye on your reference pictures. It is also better ethics in a restoration project to leave intact what is intact and only filling in what's really missing.
I really hope that will help you. I'm looking forward to see the result of your restoration project.
Rose.