What i do to clean a pony thats a little grubby is take a toothbrush with a little bit of dish soap and scrub the body. Tougher stains can be taken off usually with a qtip and acetone, however if you decide to do this take care to avoid the eyes and cutie mark as acetone will take that off. And acetone cant take off highlighter or sharpie marks if you have a pony with those.
For the hair I use a mixture of water and liquid fabric softner, dunk the mane and tail in, and then brush it out with a metal dog brush i got from walmart. Metal is better than plastic, plastic against plastic causes friction, and can make the hair frizzy.
Some people do prefer conditioner for the hair, but i find fabric softner more effective. If you only have conditioner on hand, i think that would be fine, but i would reccomend having a pony with matted hair sit with conditioner in their hair for at least a few hours, even overnight.
When brushing the pony however, be sure to start from the ends and work up to the top of the main/tail. Super tangled/matted hair when not brushed through carefully can take out hairplugs. Its normal for sone hair to shed, but hopefully not a lot.
And thats it! This is usually the routine i go through when first getting a pony. I always love beautifying them, i think its fun. I hope i didnt miss anything, i really dont think i did, but hopefully if i did another member here will correct me.
Have fun!