I think there is evidence that intermingling is quite common. Just a theory though.
Unicorns seem to be the majority in Canterlot, Pegasuseses (lol) are the only type to live in Cloudsdale, and Earth Ponies lives on the ground (Ponyville) for instance. One of my theories is that Unicorns and Pegasi that lives in Ponyville (for example) can have different origins, which may explain why some Unicorns acts more like Earth Ponies than Unicorns as they were portrayed in "Hearth's Warming Eve" or those of Canterlot. I think Scootaloo may be a prime example, as she is raised on the ground and have probably never been to Cloudsdale at all. Either her parents don't enjoy the sky, or one of them were unable to reside there..
We saw in Heart's Warming Eve that the three types became friends and probably meshed together from that day. It would be impossible to NOT see intermingling.

I think Rarity's father is infact an Earth Pony, and I find it hard to believe that "crossbreeding" is impossible.
Isn't this only canon in previous generations of My Little Pony?
I wouldn't look at it as crossbreeding as there's really nothing being shared as the child becomes either an earth, unicorn, or pegasus pony depending upon the mother/father. Only way this "might" differ is if you go into the genetics *sweet my realm of expertise

* where you have dominant and recessive traits. It is unusual to see however in RL in African Americans there is a "slim" possibility for them to have a child born to them that is white. There have been documented cases where both parents are African American yet they have a white child born to them which is....interesting however I WILL NOT go into that there as it deals with a bad subject.
Dealing with MLPFIM I wouldn't have a doubt in my mind that there's a possibility that Scootaloo might have been born to a pair of parents UE, UU, or EE having a pegasus offspring. Another sad theory that is floating around is Scootaloo is adopted due to various reasons since we've never seen her parents. Personally i'm hoping that Scoot is somehow related to Rainbow Dash which will be revealed in the show being a relative of sorts.
Another interesting theory floating around is that members of the Mane6 have alicorn blood in them which is why they are so strong. Twilight for her magic, RD for her sonic rainboom, AJ for her strength *nearly as strong as Big Mac*, etc... .
Main reason I mention this is I find it quite odd that we really haven't seen anything correlating this in the show. Most pairings are Earthx2, Pegasusx2, or Unicornx2 however I am hopefully that Rarity and Sweetie Belle's parents are the difference opening things up a bit.
As for pegasus foals being raised on the ground this I find to be quite acceptable since their wings probably haven't developed properly. When we see Fluttershy and RD in the flashback for The Cutiemark Chronicles both of them seem to be in that 10 to 12 pre-teen years type of thing. If I had to even remotely guess the kids at the school with Cheerilee are probably 4 to 6 years old maybe 8 at the most *snips maybe 7 pushing it a bit*.