Yes and no,.
Some base commanders are making it very difficult. If you own your own private gun and keep it off base, some commanders are saying you must register them anyway on base. Some are even saying you can not own anything more than a 22. It has gotten so bad, Congress is considering a law to restrict what the Commanders are doing. The following is under debate but probably will be inserted in the next Defense Budget Bill to stop the Commanders from denying service members their rights.
"SEC. 1062. PROHIBITION ON INFRINGING ON THE INDIVIDUAL RIGHT TO LAWFULLY ACQUIRE, POSSESS, OWN, CARRY, AND OTHERWISE USE PRIVATELY OWNED FIREARMS, AMMUNITION, AND OTHER WEAPONS.
(a) In General- Except as provided in subsection (c), the Secretary of Defense shall not prohibit, issue any requirement relating to, or collect or record any information relating to the otherwise lawful acquisition, possession, ownership, carrying, or other use of a privately owned firearm, privately owned ammunition, or another privately owned weapon by a member of the Armed Forces or civilian employee of the Department of Defense on property that is not--
(1) a military installation; or
(2) any other property that is owned or operated by the Department of Defense.
(b) Existing Regulations and Records-
(1) REGULATIONS- Any regulation promulgated before the date of enactment of this Act shall have no force or effect to the extent that it requires conduct prohibited by this section.
(2) RECORDS- Not later than 90 days after the date of enactment of this Act, the Secretary of Defense shall destroy any record containing information described in subsection (a) that was collected before the date of enactment of this Act.
(c) Rule of Construction- Subsection (a) shall not be construed to limit the authority of the Secretary of Defense to--
(1) create or maintain records relating to, or regulate the possession, carrying, or other use of a firearm, ammunition, or other weapon by a member of the Armed Forces or civilian employee of the Department of Defense while--
(A) engaged in official duties on behalf of the Department of Defense; or
(B) wearing the uniform of an Armed Force; or
(2) create or maintain records relating to an investigation, prosecution, or adjudication of an alleged violation of law (including regulations not prohibited under subsection (a)), including matters related to whether a member of the Armed Forces constitutes a threat to the member or others.
(d) Review- Not later than 180 days after the date of enactment of this Act, the Secretary of Defense shall--
(1) conduct a comprehensive review of the privately owned weapons policy of the Department of Defense, including legal and policy issues regarding the regulation of privately owned firearms off of a military installation, as recommended by the Department of Defense Independent Review Related to Fort Hood; and
(2) submit to the Committee on Armed Services of the Senate and the Committee on Armed Services of the House of Representatives a report regarding the findings of and recommendations relating to the review conducted under paragraph (1), including any recommendations for adjustments to the requirements under this section.
(e) Military Installation Defined- In this section, the term `military installation' has the meaning given that term under section 2687(e)(1) of title 10, United States Code. "