I figure I would chime in my $.02
My wife and kids started out 8 years ago with just hard ice cream and store bought cones.   We did alright our first time out and realized areas where we needed to improve, made some changes (ex: making our waffle cones fresh on site ) and now we are doing so well that I recently bought a small ice cream shop for a little year round business 🙂
 
Something to consider with your capital is that most events want you to prepay decent sized deposits months before the actual event.    This can really tie up the capital.
 
We do strictly ice cream, cake cones and fresh made waffle cones, and floats, and then this year to capture a bit of morning traffic added fresh made waffles.

One suggestion on figuring out what to sell?
Contact a large event in your area that you would be interested in selling at, see if there is a product that they are looking to have, or perhaps a vendor that is not returning for some reason ( hopefully not poor sales )
We do all of our events under canopies…( this allowed us to snag some indoor shows that could not handle trailers.
IF your HD offers an annual permit go that route for sure.

Shaved Ice is nice…great markup, easy set up, and does awesome on those hot summer days
 

Here is my specific situation. I am a mother, former Social Worker, now stay at home mom. I am looking to supplement my families income a bit. So not looking to get rich and not looking to replace a full time income.

I wonder how many people here will understand the humor in the following: You will find that operating a food cart will pay much better and be much less work than being a social worker.
 
Adding to give some useful info: I see you are operating out of Ohio. One thing you have going in your favor is that, as a former social worker, you (theoretically) have far greater skills in navigating bureaucracies than most (hell, once you start, you might be able to make another income helping other mobile food sellers get through health department red tape; I’ll bet a bunch of people here would hire you in a second). I notice that, in all this, there has been no discussion about health department requirements. Here’s the Cincinnati mobile food licensing application (along with regs):
http://www.cincinnati-oh.gov/health/downloads/health_pdf39560.pdf http://www.cincinnati-oh.gov/health/downloads/health_pdf39560.pdf
 
Bart

Hi HP and welcome, We have gal on this site that does mini donuts from a donut machine. She started doing Ice cream and then bought a used machine, she does a great business at a Flee market. How could you go wrong with hot dough, cinnamon and sugar. I think you should figure out  your menu, your set up will follow. The HD may have different requirements for different menu items…………….take care….Bill

We started several years ago with a 10’ x 10’ canopy, folding tables, coolers and a large charcoal grill. We served hot dogs and hamburgers with the fixings. Most of the events we did where small ones costing $75 / $100. For the most part we did fairly well. The key to success is to try and book events close together so that you won’t have much waste. Our start up cost was only the event cost, cost of the grill and the supplies.
The one thing to remember is that it is going to take a little time to decide what events to do and which ones to pass on. Also keep in mind the earlier you apply for an event the better chance you will have to lock in a spot for your type of concessions. Some events are good at not allowing duplication of food items whereas others don’t care. Some events will only allow food booths.
We purchased a new 7’ x 14’ concession trailer this summer. We have it set up to serve shaved ice, lemon shake-ups and frozen desserts for warm weather festivals and are going to set it up with hot cider, hot chocolate and apple fritters for cool weather festival. We are already booking for spring festivals and have already made some contacts for next fall. We will also add some type of food items foe next years in town festivals.
For our shaved ice we purchased a complete package from 1-800-SHAVEDICE. It comes with enough supplies to get you through several festivals. Also at festivals we only serve one size of the shaved ice and lemon shake-up.
Good luck, this is a fun and exciting business.  

We have had good experiences with winter events selling ice cream.
 
If you end up doing ice cream, let me make a few suggestions.
    1)  Get your dipping cabinet put onto casters. 
    2)  We use a 12 Hole Cabinet but only offer at a max 10 Flavors.
    3)  I would not carry fat free, or NSA flavors.  You will get asked a couple times a day but not enough that you would sell enough to justify.
    4) If you are at a super busy event consider not “displaying” your ice cream and just post your flavors.  This speeds up considerably the serving process.

Best of luck!

Be really careful with booking events. Make sure that there is an agreed limit on the number of concession caterers, or you may find far too many there – also in working out what to pay, halve whatever the event organiser says the visitors will be. Regards winter – dont know if you have the same thing in the US, but car boot sales can be a stable (if short trading hours) winter income.