The free version of Adobe Acrobat Reader is all you need to hand-write on PDF documents! You can also fill & sign PDFs without needing to purchase the Pro version.
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Download and launch Acrobat Reader.
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Open your PDF in Acrobat Reader
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Choose the Draw Freehand icon from the vertical toolbar.
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Adjust the zoom to a comfortable level.
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Use your touchscreen stylus or finger to write on the PDF.
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If you make a mistake, you can select the Eraser Tool to scribble out the writing, use Control-Z on your keyboard, or select the Edit menu, and Undo.
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When you've finished writing on your PDF, select Save As from the File menu. That will save a new copy of the PDF with your writing included.