Unless you're talking about a high dollar animal ($50,000-$75,000), most sellers won't do a trial period.
Even someone willing to do a trial period will require the total purchase price upfront, as insurance against you taking off with the horse.
Trial periods are very risky for sellers, which is why most won't do them.
I agree with this poster. Although I definitely see the benefit of having a trial period, especially for a "high dollar animal", I don't know anyone who has participated in one (as the buyer or seller). I would personally never risk this when selling one of my horses. I agree with the other posters who have stated that they would allow the potential buyer to ride the horse several times prior to the sale.
Like you, I am an adult novice rider. I bought my first horse a little over a year ago. I brought a horse savy friend with me to check the horse out and I rode the horse twice before purchasing. I did make the mistake of not getting the horse vet checked first (I only required an updated coggins test). I lucked out, because the horse has not had any problems and ended up being a healthy girl, but I have a friend who wasn't so lucky when she bought a horse without a vet check.
One of the posters above stated that their has to be trust on both sides. I respectfully disagree. Sure, you hope that the seller will feel comfortable with you taking her horse and you also hope she is being honest with you, but unfortunately there are many unscrupulous people in this world. You need to protect yourself. The seller may be a wonderful person who cares about her horse and is uncomfortable with a trial. This doesn't make her a scam artist, but it does mean that you may want to ride the horse several times with your trainer present before you purchase. Get the horse vet checked and ask for previous vet records and talk to her vet.
Another option is to find a horse that you can lease for a few months before purchasing to make sure you are a good fit.
Good Luck! I hope you find the horse of your dreams and it works out!