Is there much money in becoming a farmer, owning my own land and growing crops and raising some livestock?

I live on a farm and we are barely getting by. Absolutely no one is interested in livestock. Especially Holsteins (milk cows) and longhorns.

Farming is a business.  Like any business it draws upon all sorts of skills.  In fact, farmers have to have an extremely diverse set of skills.  The better you understand the business the more likely you are to succeed.  Farming requires long hours at certain times of the year and at other times you may have little to do.
You need to love it to make it work.
Currently it is a very good idea to seek a degree in the area you are working in.  Farming is pretty high tech and the more you know and the more knowledgeable people you know, the better off you are and the more likely you are to succeed.
Farming is cyclic in that there are very good years, very bad years, and a bunch of mediocre years in-between.

I left for college not knowing if I was going to return to the farm.  I studied Biological and Agricultural Engineering.  I figured that it would give me a lot of opportunities if I chose NOT to return to the farm.  I received a BS, MS, and worked for a while on a PhD.  Finally I returned to my family farm.  Within a short period of time I developed several products for my own use on the farm (particularly in regard to plant production in greenhouses) and eventually started a manufacturing company to sell them nationally and internationally.  It has worked out well since the manufacturing is seasonal from November to March and my farm work is mainly from April through November.
Anyway, I highly recommend you getting a degree.  It will be of great use to you whether or not you continue to pursue farming.

One more thing ...  There is a saying in Real Estate ... "Location, Location, Location"  The same it true with farming!
You can be the best farmer in the world but if you choose to farm in areas subject to drought/flooding, areas with poor soils, or areas with poor marketing potential you are doomed to failure.

One final note:  Remember, it is not how much money you "make" that counts, it is how much of it you are able to hang on to!  It is not difficult at all to GROSS a million dollars a year in a farming operation but it is extremely difficult to NET a million dollars a year.

Depends on your definition of "much money".  If you do get cattle, I would stay away from the longhorn and anything of the milk cows (as said).  I would go with some of the beef cattle, such as angus, limousin, hereford, gelbvieh, . . . Typically black angus cross cattle do a little better at the livestock auction or at least in my area it does it might be something different in your area.  

As far as the farming, equipment isn't cheap unless you get really used equipment(at an auction) and then it may not be cheap.  It takes a lot of money to get started in farming (land, equipment, fuel, repairs. . .) and often you don't get much in return.  You can make some money at it if you are careful.

Anyways that my opinion as a farmer/rancher on the  drylands of Colorado.