This is purely up to the party leaders to decide. An example in the latest primaries is Florida, which was not allowed by the Democratic Party to take place in the primary as punishment for moving up their primary voting date.
closed primary
closed primaries prevent "crossover voting"; open primaries allow it, which can produce nominees that don't represent the values of the party
In a closed primary only registered party members are allowed to vote for the candidates of a particular party. There are 13 states with closed primaries.
I got this one right: Open primaries allow any voters to participate, while closed primaries are restricted to party members. Apex - United States Government (2018) 5.2.2 Quiz: How elections Work
Thirty-four US states and the District of Columbia hold presidential primary elections. There are three types of primaries, open, closed and mixed.
party primaries
Most states prefer to hold their primaries between February and June, with March being the most common month. This allows them to have a significant impact on the selection of the party's nominee while avoiding conflicts with major holidays and events. Additionally, some states choose to hold their caucuses instead of primaries, which can have different scheduling preferences.
They choose the best looking canidate, and take them out to lunch to see how they act.
"Most states conduct CLOSED primaries, in which participation is limited to voters registered or declared at the polls as members of the party whose primary is being held" (Thomas E. Patterson, "The American Democracy", Textbook 8th ed., p. 227, emphasis added)
Wisconsin, for one.
At the moment there are about 16 States left to vote. The biggest state still to vote in the primaries is Texas with 228 delegates. Other important states yet to vote are Pennsylvania with 188, Ohio with 161 and North Carolina with 134 delegates. Texas and Ohio will vote on Mar 4, Pennsylvania on April 22 and North Carolina on May 6. In total these remaining big states make-up 771 delegates. The total of delegates of the other 12 smaller states is 480. So we just might have to wait until June 7th when Puerto Rico the last state casts its vote before it is clear which Democractic candidate (Hillary vs. Obama) wins the primaries or it may be left to the super delegates (whoever they are and however that works???). For more info see: http://politics.nytimes.com/election-guide/2008/primaries/democraticprimaries/index.HTML
yes, I'm almost positive. no,some hold caucuses