Wrong! LO does nor “export” characters. It just copies the encoding to the output file. By default, fonts are not embedded in the PDF (to reduce file size). Emoticons are not present in many font files (again to have a font file of manageable size). Thus, you must request font embedding, where the used characters (and only them) are stored in the PDF, so that the glyphs will display correctly in the case the desired font is not installed on the reader’s computer.
If PDF emoticons don’t display on your own computer (where the required font is assumed to be installed), something else is at stake. So provide a 1-page sample with clear indication of needed font. Attach both an .odt and the corresponding .pdf. To circumvent an AskLO site limitation, change the latter file extension from .pdf to .pdf.odt.