Mosfet suggession for large drain current Sample Hold application
While a schematic of the application, and the solar panel voltage, would make it simpler to provide a definitive answer, here is how one could select a suitable MOSFET:


MOSFET should (ideally) switch on hard at the MCU's GPIO output voltage. Let's say 3.3 Volts, so we are looking for a logic level MOSFET, one designed for 3.3 Volt operation. The Gate-Source threshold voltage VGS(th) for such MOSFETs would typically be below 1 Volt.
MOSFET Drain-Source voltage rating should be significantly higher than the expected voltages in the application. If the solar panel in question operates at say 10 Volts maximum, I would look for a MOSFET rated for VDS of 20 Volts, fairly common.
MOSFET drain current rating should be significantly higher than the expected drain current. For 3.2 Amperes, I would limit my search to MOSFETs rated to 5 Amperes or higher
The power dissipation at the MOSFET during full conduction needs to be dealt with, either via heat sinks, other forms of cooling, or simply by keeping the power dissipation well below the rating for the MOSFET package without heat-sink. Since through-hole was specified, the common MOSFET package of TO-220 would typically be quite safe at 0.5 Watt dissipation, and would run hot but probably not too badly at 1 Watt, without a heat sink. To achieve this, one would look for a MOSFET with on resistance RDS(on) of under 49 milliOhms (501 mW) or at worst, 100 milliOhms. A heat sink allows far greater latitude, of course.
Given the rather relaxed timing requirements, switching losses are not much of a concern, nor is switching speed or gate capacitance, really.


So, given the above parameters, a search on Digikey yields at least 79 results as I just checked. On sorting by lowest price for single unit purchases, a couple of options are:


IRLU2703
STD95N2LH5


Of course, if SMD were an option, many, and less expensive, options would open up, including some excellent devices by Alpha Omega and International Rectifier. 



As pointed out by Russell, if providing a gate drive voltage higher than the MCU power rail is not a problem, and a P-channel MOSFET is preferred, then a similar Digikey MOSFET search yields several P-channel MOSFETs that meet the specifications above, setting aside the VGS(th) point. For instance:


FQPF27P06
irfr5305