I have added a brief Walkthrough for the first week of the game to my 1st Year Events Calendar Guide for HM Cute DS but the updated version of the guide may not have been published yet by IGN. I believe I should add one to my 1st Year Events Guide for the original Boy version of HM DS as well. It offers many useful tips to make the game easier for players.
One of these is a way to obtain a horse on the very second day of the game. You need to spend a little time in the Excavation Site digging for jewelry, but you should do that anyway!
On Monday, 2 Spring, the day on which the game begins, the Supermarket will be open but you will have only 500G which should be spent on seeds. Never mind that. Van will come to the Valley on the 3rd to open his stall on the 2nd floor of the Inn. There you can sell jewelry from the Excavation site for up to 3250G each.
Do not forget to buy at least one item from Karen's Supermarket each day it is open for the first 10 days in order to rescue the Sprite who runs the Shopping Network.
When Tuesday arrives, you can obtain the horse from Takakura by shipping 1000 items. This is easily done as follows:
Buy Bird Feed from Popuri and dump it in the shipping container. You can carry 99 portions of Bird Seed in every empty slot in your rucksack. Even though you will have only 18 slots in the small rucksack, it will not take long to ship whatever amount of Bird Feed is required to bring your total to 1000. As soon as you throw the 1000th item in the bin, you will rescue a Sprite. Go into your house then and when you exit, Takakura will be at your door with a Horse.
It's as simple as that. Even after investing in the Bird Feed, you should have more than enough money to order the first Bird Barn from Gotz.
The horse is not really that useful once you have a teleport stone but until Sunday, 8 Spring when the Casino is unlocked, the horse will make your life MUCH easier!
Unlike some of the other Harvest Moon games (FoMT/MFoMT and Harvest Moon Boy & Girl come to mind), the horse can be ridden anywhere outdoors on the map. Riding the horse will cut your transportation time in half until you have the very useful teleport stone.