The minutes showed members were concerned that the incoming president would adopt policies designed to increase economic growth that would require faster interest-rate increases.
But they also urged caution over the "uncertain" outlook.
The Dow Jones Industrial Average was up 0.30% at 19,942.16 points.
The S&P 500 gained 0.57%, rising to 2,270.75. The Nasdaq Composite added 0.88%, finishing at 5,477.00.
Chris Low of FTN Financial in New York said: "the market was right in thinking the minutes would tilt hawkish, but they tilted less than expected".
The minutes said that policymakers discussed "the uncertainty about how federal spending, tax, and regulatory policies might unfold and how global economic and financial conditions will evolve."
President-elect Mr Trump takes office later this month and investors are waiting details of his policies, which are expected to include cuts in taxes and increases in infrastructure spending.
US shares have rallied since Mr Trump's election victory as a result.
Shares in carmakers also helped the market move higher on Wednesday, following better than expected December sales figures. General Motors shares rose 5.5%. Ford shares rose 4.6%.
Tech giant Apple has confirmed plans to invest $1bn in a tech fund being set up by Japan's SoftBank.
SoftBank has said it is investing at least $25bn in the fund and has been in talks with Saudi Arabia's Public Investment Fund for an investment that may reach $45bn.
Wall Street held onto gains after minutes from the Fed's December meeting showed policymakers were more cautious than expected over future rate rises.