Usually your paste mask would not expose the through holes. The reason I didn't elaborate further was because I interpreted the question as not being as nuanced as some of the others who chose to answer.
Elaborating (by popular demand), when you design a PCB in virtually any modern Electrical CAD package (Eagle,KiCAD, Mentor Graphic, Altium, Cadence, Zuken, etc.), the last step(*) before sending your board off to be produced is to generate the "layer artwork" (aka Gerber files) which the PCB manufacturer can use to construct your board.
One of those layers will be the Paste (aka Cream) layer for the top (aka Component) side and one for the bottom (aka Solder) side of the board. Those two layers are of no value to the PCB Manufacturer. They are, however, of interest to whoever is doing your PCB Assembly, as they will typically use these files to make a stencil over which solder paste can be dragged to deposit solder paste on all the exposed pads where components will be placed (often by a Pick and Place machine, but also can be by hand for small designs / volumes) prior to going through a temperature profile controlled Reflow process. Almost never (in 2019), I would say, are the through-hole pads (where your through-hole components will eventually be populated) exposed in this solder stencil, and therefore no solder will be deposited on those pads, and there is very little risk of solder flowing into them or their associated holes during reflow.
The risk of reflow is further mitigated by another one of those Gerber layers, called the Solder Mask layer. During PCB manufacturing this layer acts kind of like another stencil to define where not to apply a layer of film that is solder-phobic (it won't bond to it). Usually both through-hole pads and the surface mount pads are exposed through the solder-mask layer, and the solder mask exposure is a tiny bit bigger than the solde so that you can weld the components to the PCB with applied solder paste and hand soldering.
Because of these two factors, the chances are you will very likely not experience any problems whatsoever first doing SMD reflow and then subsequently populating and soldering through-hole parts.
(*) Many manufacturers these days will accept a native design file from these tools (e.g. the .brd file from Eagle) and synthesize the Gerber artifacts themselves. I find it a good idea to do this for myself anyway and review the Gerbers for myself in a Gerber viewer, but depending how much you trust your manufacturer, that might be considered "old school."