This is a really interesting question! What you have here is the so-called "bare infinitive." A bare infinitive is when the infinitive, in this case "to go," drops the "to" but still functions as an infinitive. The bare infinitive always follows verbs like would, shall, may, and must, but as in this case, can also follow certain other verbs like let, make, and to hear. Go seems to have become one of the those verbs. It seems to happen a lot in conditional cases like the one you ask about.; for example, "I would rather eat nails than study more English!" Here are some more examples both formal and informal. Consider I bade him go. You must learn English. He had better ask permission. Let her stay there. I heard him speak the words. I would definitely say and write "How about if we go see."

'Go see' is only used in informal American English. Elsewhere, English speakers say 'Go to see....' or 'Go and see...'.

Good question :) As a native English I don't have an exact answer, but it seems like "go see" is just an abbreviated version of "go to see" and "go see" is more commonly said because it's easier and more natural to say

"How about [if] we go [to] see that movie?" You may remove either word without affecting the meaning, or even remove both. However, removing the "to" definitely makes it sound less formal, but it's very common. I personally would always remove the "if".

Hmmm i think the correct way to say it is " go to see" !