Does the Red Queen's face intentionally evoke Mickey Mouse?

As with many adaptations of Lewis Carroll, the characters of the Queen of Hearts and the Red Queen have been combined.

Thus her hair is in the shape of a heart. Any resemblance to Mickey Mouse is coincidence.

The widow's peak is a common appearance, especially for villainous characters, and also makes her face more heart-shaped.

The concept art looks even less like Mickey Mouse.

No, nobody has ever explicitly confirmed nor denied this, for the same reason nobody has explicitly confirmed nor denied whether her hair was intended to look like a pretzel.

According to hairstylist Terry Baliel, the wig for Helena Bonham-Carter was specifically designed to look like a heart. Any resemblance to the shape of Mickey Mouse's head would appear to be a coincidence, and therefore unintentional.

Hair: “Helena’s look was hard and structured,” says Baliel. “We wanted the wig to be heart-shaped — we built some mesh pads and combed the hair, strand by strand, over that, ending up with curls on top so it almost looks like a bouquet of roses.

Here is a link to the interview where the costumes & hair design for each character are discussed:

http://nypost.com/2010/02/28/how-fashion-and-beauty-visionaries-brought-alice-in-wonderland-to-life/

History:

With a little more research, we find that both The Queen of Hearts as well as her enemy The Duchess had heads that were roughly heart-shaped due to their headdresses, which are notably Elizabethan in origin. This interpretation of the character goes back to the original 1871 Tenniel illustrations:

It's important to note that the actual text of the books never describes her head as such, or even gives much of a physical description at all.

I agree with @OrangeDog that the heart-shaped hair is intended as a reminder that this character is both the Queen of Hearts and the Red Queen. However, it might also be an exaggerated version of the hairstyle found on a famous portrait of Queen Elizabeth I.

This is attested to by Valli O'Reilly, an Oscar-winning makeup artist who worked on Alice in Wonderland, as reported by the New York Post:

"Helena [Bonham Carter] took longer because we had to have a prosthetic piece put over her eyebrows," says [Valli] O'Reilly. "Tim [Burton]'s notes to me and Helena were: Bette Davis as Queen Elizabeth, in that 1939 movie where she had red hair and her forehead was really high and the eyebrows might even have been shaved off."

Here's a short video clip and a photograph of Bette Davis from The Private Lives of Elizabeth and Essex (1939), which is likely the movie referred to, from Stalking the Belle Époque: