The original source for the 3:1 number is military.com, and it is worth looking at the source. The poll is from Oct. 24 - Oct. 31 2016.
Career-oriented troops favor Republican presidential candidate Donald Trump over his Democratic opponent Hillary Clinton by a 3:1 margin, a new Military.com reader survey has found.
Trump's lead narrows when the results are filtered for the active component. For example, among only active-duty respondents, 63 percent said they plan to vote for him.
Military.com conducted a voluntary online survey of readers [...] The sample is not a perfect representation of the military as a whole. It includes a higher percentage of airmen, soldiers, officers and noncommissioned officers, and a lower percentage of women, minorities and junior enlisted personnel than are in the force.
NBC News also had a poll around the same time via survey monkey (see here). The poll is from Aug. 29 - Sept. 4 2016.
Donald Trump leads Hillary Clinton by 19 points — 55 percent to 36 percent — among voters who are currently serving or have previously served in the U.S.
A sizable number of military and veteran voters say they would not be confident in Clinton or Trump's ability to be an effective commander-in-chief of the nation's military — but a slight majority would be confident in Trump (53 percent).
Militarytimes.com also had a poll (also online, and also unscientific like the military.com poll). The poll is from Nov. 10 - 14 2016.
The poll surveyed 2,790 active-duty troops. Among those who voted, 51 percent said they supported Trump.
They also had a number of previous polls (eg here or here). qz.com notes that the high percentage for Trump is mainly due to the demographic markup of the military (more men than women).
Fox News also had a poll. It did not ask active military personell, but veterans. The result was 46% for Trump, 34% for Clinton.
The claim that exit polls show 60% for Trump is correct. Looking at the military.com poll, the fact that many voted by mail would likely reduce that percentage, not increase it, as those currently active are more likely to need to vote by mail, and according to that poll, they are less likely to vote for Trump.
There do not seem to be any polls that are more recent than these.