Addressing the drop-in-credit-score item - as noted in another answer, the FICO scoring model treats multiple score pulls within a short period of time for a particular purpose as a single pull. They expect you to be shopping around for a loan on a large purchase such as a car or house. That said, the credit pull will likely cause a drop of between 5 and 10 points on your score, for between one and two years. This drop is insignificant on a credit score in the 800+ range, and any credit score is insignificant if you do not need to apply for new credit.
As a side note, the FICO model is not one single model, but several which are optimized for particular types of lenders. You might have a different score for a home mortgage, car loan, and credit card, for instance.
As for whether you would be approved for a loan - well, the underwriting guidelines will differ between institutions, but overall the determining factors are "credit-worthiness" and "ability to repay". Your 800+ FICO score implies good credit-worthiness. Your ability to pay is determined principally by your income and by your debt-to-income ratio. Since you say you have an outstanding mortgage of $100k and only note yearly income of $25k, the odds are that your debt-to-income ratio will not look good. Assuming your current mortgage payment is based on a 30-year loan for $200k, you are looking at a ~$1000/month payment exclusive of interest, taxes, and insurance, which is about 50% of your monthly take-home before considering regular expenses or other debt. A debt-to-income ratio of 36% or 43% is typically the ceiling for mortgages (depending on pre-tax or post-tax numbers). You are not yet qualified for Social Security or most pensions, and cannot touch 401k or IRA assets without high tax penalties (or special circumstances) so if, as I suspect, a large portion of your assets are tied up in such funds, they do you little good in this case.
You have the enviable position of having a large pool of assets. This does change your situation, but those assets are not encumbered in any way. You could, should you so choose, give them away, sell them, lose them gambling, or (in the case of the investments) lose them simply in a market crash. Unless you pledge some of those assets as surety for the mortgage debt (thus putting a lien on the property) or you have additional income beyond what you have specified from investments, your approval chances are lower than you might like - depending on the size of the mortgage you wish to take out and whether you actually sell your current home (eliminating that debt) before buying the new one (mortgage closings can be structured to account for this - it is very common).
You can probably find a lender who is willing to work with you - your asset accumulation is sufficient to demonstrate financial stability. As suggested above, this may involve a higher down-payment, partially securing the loan with other property, or some other financial arrangement.
You may find it better to pay for your new home outright and consider a HELOC if you need. This would have the alternate effect of reducing your yearly investment income, which may not be something you can live with. Conversely, that may be offset by the elimination of your current mortgage debt.
