Making Mom Friends

This is sort of embarrassing to say, and I wouldn't say this to too many people, but being a mom is lonely. I mean, I am with Sister Bear all day long, and see Papa Bear everyday and Brother Bear every other day, but I am lonely for friends. People who can relate to me and my life. People who want to talk about babies all day long but understand that sometimes I want to talk about other things as well. People who know what a big deal it is to walk up to the coffee shop and get out of the house for 4o minutes or so.
I have friends that have babies and kids, but no one that lives close. And no one that I feel I relate to, as a mom. Is that weird? I think it is....
We moved in September to our new house and I love it here and have met the neighbors and have become friendly with some of them, but there is no one (yet) that has become the type of friend that comes over for coffee, or for wine, just to hang out so our kids can play on the floor while we chat. That is what I am looking for. I don't think it is too much to ask. I am just not sure how to get to that point with someone. It's like dating all over again, without the joy of the first kiss. Ha Ha.
I go for walks around the neighborhood a few days a week, keep my eyes open for other moms. There always seems to be people pushing strollers down the street, but I never approach them. If they would approach me, I would love it, but how do I know they feel the same way? Maybe they have oodles of mommy friends and don't need another one.
We have a park near our house, and I recently took the kids there. I was so excited when we approached and I saw two other moms there with young kids. Brother Bear started playing and attempted to play with the kids, and I don't want to sound mean, but the kids were very unfriendly to him. To the point where I was uncomfortable, wondering how these moms could let their kids act like this. These were not the type of moms I was looking to meet. We moved on to another play structure and encountered other kids and moms but nothing happened. No conversations were started (umm...excuse me? Don't you see this adorable baby in my stroller? Don't you want to ask how old she is? What is her name? Anything?? Want to be my friend? I have wipes to share! Diapers? Candy? Guess not.....)
This is depressing even writing this. I guess if I want friends so bad, I need to take the first step. Use the old "We are new to the area" approach and see where it gets us. Our community has a reputation of being a bit....snooty I guess is an appropriate word, but I assumed we would meet the next generation of families, the ones like us, friendly, beer drinking, flip flop wearing, pizza eating real families, looking for real relationships with neighbors.
Any suggestions?
Some of my moms friends suggested having a party at our place when the weather heats up to reintroduce ourselves to the neighbors, which sounds like a good idea, but I get so nervous doing stuff like that. What if it's a flop? What if no one comes, or what if we don't click with anyone. I would be so deflated.
Ok I need to just let go of my fears, I really have nothing to lose.
I am sort of holding hope that when Sister Bear starts school I will make friends with other moms from her school...but jeez that is like 4 years from now. I need something before that.
I will keep you posted on our friend finding adventures.