A cool and somewhat easy mount to obtain is the War Horse: https://www.tibiawiki.com.br/wiki/War_Horse
But you will need to have some luck on finding Wild Horses, they are available only during this world change. they spawn every 3 hours after the server save if the world change is happening: https://www.tibiawiki.com.br/wiki/Horse_Station
Be aware that you should look to tame Wild Horses only, not normal Horses!!! Horses cannot be tamed.
They usually are located east of Thais, near Palomino area: https://www.tibiawiki.com.br/wiki/Wild_Horse
It will take some time to you, but the best way is to fabricate your own Sugar Oat (mount item) in order to save money! Go to Liberty Bay, on the Sugar Cane plantation area. Bring with you at least 10 firebugs and a sickle. First put the fire bug on the cane and after you can harvest it with your sickle and obtain the bunch of sugar cane! Be aware that the Firebug can explode after several times using it!
Do the maximum possible of it! After that, you need to use the bunch of sugar cane on a bunch of wheat (easy to find a wheat plantation right by Palomino, on the east exit of Thais. Remember to bring a scythe in order to harvest wheat) and you will obtain the Sugar Oat! Now you just need to trap the first horse that you see and use the sugar oats until it works!
The more Sugar Oats you make, the better is for you! You will own already sugar oats reserved for another character grab a horse at the first opportunity! They can be sold at the market as well!
On this video, it took almost 40 Sugar Oats to tame the Wild Horse! Still, it can be somewhat cheaper the sugar oat fabrication, specially if you live or hunt on Liberty Bay: https://www.youtube.com/watch?v=1LM_H937upg
References used: https://www.tibiawiki.com.br/wiki/Sugar_Oat