OK, that foreground vehicle is the Surrey. So what's that other horse-drawn conveyance next to it? A jitney? A buckboard? They certainly appear to be popular with the 1958 crowds, and at a mere ten cents for a ride, it is no wonder.
Over the years there have been a number of Main Street vehicles that have been retired, including the Surrey. One friend of mine misses the traffic, but it seems that when I visit the park, there are so many people crowding the streets that it is hard to imagine the addition of horseless carriages, surreys, and chemical wagons.
On a side note, in older park photos I've noticed that most Disneyland guests stuck to the sidewalks, just like on a "real" street.