Looking for Games to Play for My 3 y.o. Birthday Party

At this age winning/losing games are very likely to bring tantrums. I would discourage you from trying any of those.
If you can have a sandbox and an inflatable pool in your yard it would be great! The pool needs to be supervised 100% of the time, as little ones can drown in 2 inches of water. A samll picnic table with playdough works too. Sidewalk chalk, or a giant piece of paper and watercolors keep litle ones entertained. For all of the above you can choose "princess" colors: pastels, pinks, purples, as well as glittery ones. Bubbles are a good option, too. You are lucky that you can have your party outside, as all these messy options would be a disaster inside your house.

For the 3yr olds, large beads to thread onto pipe cleaners is a fun activity. We'll be having a table for this activity at my own daughters 3rd bday party this weekend. Someone had suggested bubbles, at a party we went to recently they all got spilled out pretty quickly, so if you can purchase a battery bubble blower, that works great. A friend bought my daughter one for her 2nd bday and we opened it up right away. Another option is the water table, a huge hit for kids of all ages. Have fun, relax, most kids this age are happy to run around (monitored) yet unstructured.

I agree that you want non-competitive play instead of games with winners/losers. Can you collect enough dress-up clothing & toy instruments for a princess parade? All the kids can dress up, grab an instrument and parade around the yard. Since parents will be present you could set up a simple craft table (make your own princess crown?).

Have a great day!

Kids that young are happy with singing and dancing. If you know any motion songs those are good. They are easily entertained. For example if you just get a bunch of balls in a bag and throw them all over the yard and tell them to hurry up and pick them up and beat the clock they will love it. It doesn't even have to be balls it can be other items.

I live in Mt. Kisco and the library in Katonah has a great storytime although I haven't actually been there because I work and it's always canceled when I am off (b/c I work in a school)So when I am off other activities are also off. But anyway I have heard it's good and it's a great way to meet other moms.