I'm in the same game as you, doing pet portraits for a 'living' aka paying my way through uni, and have been doing commission work for the last 4-5 years.
I'll run through what I've noticed with your site page by page, makes things easier!!
Title/business name and logan. Do you want to draw only horses, or branch out into the wider community of cats and dogs? You'll pick up more work doing cats and dogs rather than restricting to horses, so try to come up with at least a 'slogan' that shows you draw all types of pets, not just horses.
Home page: I'm not sure if it's just my laptop or something wrong with the link, but I think you've tried to post of photograph on you home page and it is just coming up as a jumble of letters/symbols. Might want to check that out.
Meet the artist: This page sounds quite amateur-ish, to make a more professional 'sounding' page, try to write in the third person when describing yourself, so instead of 'I' use 'her' etc. You have got quite a few grammar and spelling issues in there, have a close look through and get a friend to proof read it for you and point out mistakes. Avoid writing I instead of I.
Avoid stating your exact age, and don't say that most of your portraits have been dogs, clients don't need to know that. I also wouldn't say that your commissions begun via a computer game, try to word it a little 'classier', maybe by saying your begun drawing friends/family's pets and went from there.
Orders and Pricing: Again, your use of language comes across in quite an unprofessional and disorganised manner. You're not giving prospective clients any 'out-room' by demanding straight up a $50 deposit, you need to talk it over with clients and allow them to 'warm-up' to you. I have a 'disclaimer' section at the bottom of my rates page that states I require a 20% deposit prior to commencing work, and that I will happily refund 100% of this is the client changes their mind before I commence. The fact that you've said you need their deposit to buy supplies makes me turn off a little, be careful with how you word things!
To get the best possible portraits, you need to work with your client, talk to them and see what they want, find out a bit about the pet etc. so it seems like you're genuinely interested in their animal. Your client will warm to you and usually be better to deal with if they think you're in it for the enjoyment rather than the money.
When I deal with clients, I keep everything organised and professional, everything I need is spelled out in simple dot points/short sentences to make it clear exactly what I require of my client to begin my work.
You need to make obvious what currency you are working in, US$, AU$ etc.
The first size option you list is '9X12 portraits'... then the rest just give the size, either stick with 'portraits' at the end, or take 'portraits' off the first option. Also state you you are working in inches or cm's.
Rather than saying 'oil painting' just say 'oils' or 'oil paint'.
If you work in graphite pencils, or coloured pencils, you have to say so. Black and white pencil is graphite, so advertise as 'graphite' to make it clearer and sound classier.
I'm finding it a bit confusing and difficult to work out your price list, it has to be straight down the line and bold, you've got a bit of fiddling to do on this page.
Oder form: Ok, people want to do things online these days. Obviously if you have a website you've got an email. Connect your order form to your email, or recommend that people contact you via email with their photos and details.
Check is in fact spelt 'cheque' when referring to a money cheque. Cheques cost people a decent amount of money to make out, and many will be hesitant to do so as it is a hassle. Give other options of payment, money order, paypal (paypal accounts are very easy to set up and very useful for payments!), direct deposit (set up internet banking with your bank so that clients can deposit money directly into your account).
Try to keep all correspondence by email, or supply a mobile/cell phone number for people without email to contact you by. That way you don't have to give out your residential address to any old person who comes across your website.
Have a look at my site for a bit of an idea on how to go about the suggestions I've given you. Unfortunately my site is also a freewebs site, due to my registered server not working for me, however freewebs is working quite well at this point in time and I have been very busy with commissions coming in. Home - Horse & Hound Artistry