[edit] Pony breeds
Main article: Pony
Ponies are usually classified as animals that mature at less that 14.2 hands. However, some pony breeds may occasionally have individuals who mature over 14.2 but retain all other breed characteristics. There are also some breeds that now frequently mature over 14.2 hands due to modern nutrition and management, yet retain the historic classification "pony." For the purposes of this list, if a breed registry classifies the breed as a "pony," it is listed here as such, even if some individuals have horse characteristics.

(Please note: Because of this designation by the preference of a given breed registry, most miniature horse breeds are listed as "horses," not ponies)

American Shetland, see Shetland pony
American Walking Pony
Ariegeois pony or Ariègeois
Assateague Pony, see Chincoteague Pony
Asturian pony
Australian Pony, also known as Australian Riding Pony
Avelignese Pony
Bali Pony
Bardigiano Pony
Bashkir Pony
Basque Pony
Basuto pony, also spelled Basotho pony
Batak Pony
Bhutia Pony, also spelled Bhotia Pony
Boer Pony
Bosnian Pony
British Riding Pony, see Riding Pony
Burmese Pony
Carpathian Pony, see Hucul Pony
Caspian pony
Chincoteague Pony
Chinese Guoxia
Connemara pony
Dales Pony
Dartmoor pony
Dulmen pony
Eriskay pony
Exmoor pony
Falabella, see Falabella (horse) in horse section
Faroe pony
Fell Pony
French Saddle Pony
Galician pony
Garrano
Gotland Pony
Gǔo-xìa pony, see Chinese Guoxia
Hackney pony
Highland Pony
Hokkaido Pony
Hucul Pony
Icelandic pony, see Icelandic horse in horse section
Kazakh Pony
Kerry bog pony
Landais Pony
Lundy Pony
Manipuri Pony
Merens Pony
Miniature horse, see horse section
Misaki
New Forest Pony
Newfoundland pony
Noma pony
Northlands Pony
Ob pony
Peneia Pony
Pindos Pony
Poney Mousseye
Pony of the Americas
Pottok
Riding Pony
Sable Island Pony
Sandalwood Pony
Sardinian Pony
Shetland pony
Skogsruss, see Gotland Pony
Skyros Pony
Spiti Pony
Sumba and Sumbawa Pony
Tibetan Pony
Timor Pony
Virginia highlander, see horse section
Vyatka
Welara
Welsh pony
Welsh mountain pony (Section A), see Welsh pony
Welsh pony (Section B), see Welsh pony
Welsh pony of cob type (Section C), see Welsh pony
Yakut Pony
Yonaguni, see horse section
Zaniskari pony
Žemaitukas, also known as Zemaituka, Zhumd, Zhemaichu, or Zhmudka
References :

Grooming:
Grooming is an important part of you and your horses bonding experience. It is always fun to make your horse look gorgeous!
-Metal Curry Comb ($5)
-Rubber Curry Comb ($4-13)
-Hoof pick (w/brush on the end is nice!) ($2-4)
-Mane and Tail Brush ($5-10)
-Stiff/Hard Brush
-Dandy/Medium Brush
-Face/Soft Brush
-Sponge
-Sweat scraper
-Towel
-Bucket (for putting shampoo in)
-Shampoo
-Brush Box/Bag
-Hoof Oil

Tack:
As far as tack goes you will need a couple of different things depending on what style you will be riding. The basic tack would be:
-Saddle ($300-5000)
-Saddle Pad ($20-150)
-Bridle ($50-400)
-Galloping Boots ($50-150)
-Halter and lead rope (leather- $40-200; nylon- $15-30)
-Girth ($30-300)
-Stirrups and stirrup leathers ($75-200)
-Martingale/Breastplate ($30-250)
-Bit ($15-300)

Clothes for you:
-Spurs
-Crop
-Pants (called different things for each style)
-Boots
-Helmet
-Gloves
-Fun Tall socks
-Show Shirt
-Hairnet
-Show Jacket
-Chaps/Half Chaps
-Belt
-Stock pins

Stuff To Know:
Training:
When training a horse or pony whether they are young or old your main go is to get to the reward phase. You don’t want to torture the horse so when he does something correctly reward him with the absence of punishment. If the horse if scared of something let them sniff it or hand walk them around it.

Emergencies:
When there is a horse emergency it is very important to stay calm.
-Getting Cast
When a horse gets cast you should take a COTTON lead rope and wrap it around the hind leg the farthest away from you. Pull the horse slowly towards you, stay out of the way! Keep the horse calm, walk him for 15 min. after he is uncast.
-Breathing/Allergies
If your horse is having difficulties breathing or having a severe allergic reaction, contact you vet immediately. Try to keep the horse cool.
-Colic
If a horse appears to be colicing you should walk him till he manures. Also contact your vet.
-Loose Horses
Horses often get loose so it is important to have a plan. When trying to catch the horse bring treats, a lead rope, and a halter. Try to get a lead rope around the horse’s neck and then put the halter on him. Cool the horse down and wrap his legs. You and your barn may want to set up a series of gates so if as horse gets loose he will stay on the property.

Before you buy:
Before you buy your horse make sure he passes his vet exam, and has a negative coggins. And make sure that you found the right horse for you!

The joys of having a horse:
Having a horse is wonderful, you will love it!
References :

quarter horse
paint
thoroughbred
appaloosa (appy)
lipizzaner (lipizzan)
shire
belgian
clydesdale
friesian
arabian (arab)
akhal teke
andalusian
holsteiner (holstein)
References :
great site to look at
http://www.horseworlddata.com/breed.html

Thoroughbred
AQHA (american quarter horse)
Appendix Quarter Horse (a thoroughbred crossed with a QH)
Arabian
Morgan
Akhal-Teke
Mustang
Kiger Mustang
Saddlebred
Tennessee Walker
Cleaveland Bay
Oldenburg
Trakehner
Dutch Warmblood
Swedish Warmblood
Barvarian Warmblood
German Warmblood (there are lots of warmbloods)
Hanoverian
Holsteiner
Marwari
Appaloosa
APHA (american paint horse)
Mule
Lusitano
Andalusian
Clydesdale
Percheron
Suffolk Punch
Ardenaise
Jutland
Rocky Mountain Horse
Paso Fino
Peruvian Paso
Lippizanner
Gypsy Vanner
Morab (morgan crossed with an arabian)
Quarab (quarter horse crossed with arabian)
Fresian
Tinker
Bashkir Curley
Colorado Ranger Horse
Florida Cracker Horse
Brandenburg
Orlov Trotter
Missourie Fox Trotter
Standardbred
Irish Draught
Hackney
Abaco Barb
Alter-Real
Anglo Arab (cross between an arabian & thoroughbred)
Criollo
Azteca
Brumby

There are MANY MANY more horse breeds than these. These are just a few. I recomend buying your daughter a few books about horses. Horses are a great thing for a girl to be interested in. They keep us out of trouble, and give us something to work for. Horses are the antidrug.
References :
11 years experience studying and working with horses & training from proffessionals