I'll risk getting flamed!
I'll go against the grain and say yes, you can cattle ranch without a tractor. My neighbor does it, in fact most ranchers that lease pasture do it to some extent.
Doing the initial fencing and pond building requires the equipment. After that, you just turn the cattle out and let them graze (more on this later). When you buy round bales, they can deliver them to your site. All you need is a bale spear or buggy to move them with a pickup. Fertilizer/lime can be bought and spread using trailers supplied by the fertilizer supplier. The brush hogging for pasture maintenance can be sub-contracted.
Is this the most efficient and cost effective way to do it? It depends. For 10 - 20 head, it probably is. I can't see the returns from 20 cattle paying the note on a $20,000 tractor. For 100 -200 head, it probably isn't and a tractor's purchase is justified.
Here's the "More on this later" part:
If you have the right "cows per acre or in Texas, acres per cow" density, then they're pretty self sufficient regarding feed.
Supplemental feed's required during the months when forage growth can't keep up and may necessitate putting out round bales. But, there's a lot more to raising cattle, then just keeping them fed. You need to worm, castrate, calf etc.
You really need someone that lives close to the property that can drive by and check things at least once a week. They need to watch for theft, downed fencing, calfing, veterinary etc.